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Common Core: High School - Algebra : Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2-x-6$

Possible Answers:

$\text{x-intercepts: }2, 3$ $\displaystyle \text{x-intercepts: }2, 3$

$\text{x-intercepts: }2, -3$ $\displaystyle \text{x-intercepts: }2, -3$

$\text{x-intercepts:}-2, -3$ $\displaystyle \text{x-intercepts:}-2, -3$

$\text{x-intercepts:}-2, 3$ $\displaystyle \text{x-intercepts:}-2, 3$

$\text{x-intercepts:}-1, 6$ $\displaystyle \text{x-intercepts:}-1, 6$

Correct answer:

$\text{x-intercepts:}-2, 3$ $\displaystyle \text{x-intercepts:}-2, 3$

Explanation:

To find the $\displaystyle x$-intercept of a function, first recall that the $\displaystyle x$-intercept represents the points where the graph of the function crosses the $\displaystyle x$-axis. In other words where the function has a $\displaystyle y$ value equal to zero.

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2-x-6$

the coefficients are,

$\\b=-1 \\c=-6$ $\displaystyle \\b=-1 \\c=-6$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-3)(x+2)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-3=0\rightarrow x=3 \\x+2=0\rightarrow x=-2$ $\displaystyle \\x-3=0\rightarrow x=3 \\x+2=0\rightarrow x=-2$

To verify, graph the function.

Screen shot 2016 03 08 at 11.06.54 am

The graph crosses the $\displaystyle x$-axis at -2 and 3, thus verifying the results found by factorization.

Report an Error

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2-7x+12$

Possible Answers:

$\text{x-intercepts: }-3,4$ $\displaystyle \text{x-intercepts: }-3,4$

$\text{x-intercepts: }-3,-4$ $\displaystyle \text{x-intercepts: }-3,-4$

$\text{x-intercepts: }3,-4$ $\displaystyle \text{x-intercepts: }3,-4$

$\text{x-intercepts: }6,2$ $\displaystyle \text{x-intercepts: }6,2$

$\text{x-intercepts: }3,4$ $\displaystyle \text{x-intercepts: }3,4$

Correct answer:

$\text{x-intercepts: }3,4$ $\displaystyle \text{x-intercepts: }3,4$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2-7x+12$

the coefficients are,

$\\b=-7 \\c=12$ $\displaystyle \\b=-7 \\c=12$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-3)(x-4)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-3=0\rightarrow x=3 \\x-4=0\rightarrow x=4$ $\displaystyle \\x-3=0\rightarrow x=3 \\x-4=0\rightarrow x=4$

To verify, graph the function.

Screen shot 2016 03 08 at 12.13.08 pm

The graph crosses the $\displaystyle x$-axis at 3 and 4, thus verifying the results found by factorization.

Report an Error

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2+9x+18$

Possible Answers:

$\text{x-intercepts: }2,9$ $\displaystyle \text{x-intercepts: }2,9$

$\text{x-intercepts: }6,-3$ $\displaystyle \text{x-intercepts: }6,-3$

$\text{x-intercepts:}-6,-3$ $\displaystyle \text{x-intercepts:}-6,-3$

$\text{x-intercepts: }6,3$ $\displaystyle \text{x-intercepts: }6,3$

$\text{x-intercepts:}-6,3$ $\displaystyle \text{x-intercepts:}-6,3$

Correct answer:

$\text{x-intercepts:}-6,-3$ $\displaystyle \text{x-intercepts:}-6,-3$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2+9x+18$

the coefficients are,

$\\b=9 \\c=18$ $\displaystyle \\b=9 \\c=18$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x+3)(x+6)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x+3=0\rightarrow x=-3 \\x+6=0\rightarrow x=-6$ $\displaystyle \\x+3=0\rightarrow x=-3 \\x+6=0\rightarrow x=-6$

To verify, graph the function.

Screen shot 2016 03 08 at 12.27.49 pm

The graph crosses the $\displaystyle x$-axis at -3 and -6, thus verifying the results found by factorization.

Report an Error

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2+2x-8$

Possible Answers:

$\text{x-intercepts: }-1,8$ $\displaystyle \text{x-intercepts: }-1,8$

$\text{x-intercepts: }-4,-2$ $\displaystyle \text{x-intercepts: }-4,-2$

$\text{x-intercepts: }4,2$ $\displaystyle \text{x-intercepts: }4,2$

$\text{x-intercepts: }4,-2$ $\displaystyle \text{x-intercepts: }4,-2$

$\text{x-intercepts: }-4,2$ $\displaystyle \text{x-intercepts: }-4,2$

Correct answer:

$\text{x-intercepts: }-4,2$ $\displaystyle \text{x-intercepts: }-4,2$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2+2x-8$

the coefficients are,

$\\b=2 \\c=-8$ $\displaystyle \\b=2 \\c=-8$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-2)(x+4)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-2=0\rightarrow x=2 \\x+4=0\rightarrow x=-4$ $\displaystyle \\x-2=0\rightarrow x=2 \\x+4=0\rightarrow x=-4$

To verify, graph the function.

Screen shot 2016 03 08 at 12.52.32 pm

The graph crosses the $\displaystyle x$-axis at -4 and 2, thus verifying the results found by factorization.

Report an Error

Example Question #221 : High School: Algebra

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2+2x+1$

Possible Answers:

$\text{x-intercept: }0$ $\displaystyle \text{x-intercept: }0$

$\text{x-intercepts: }-1,0,1$ $\displaystyle \text{x-intercepts: }-1,0,1$

$\text{x-intercepts: }-1,1$ $\displaystyle \text{x-intercepts: }-1,1$

$\text{x-intercept: }-1$ $\displaystyle \text{x-intercept: }-1$

$\text{x-intercept: }1$ $\displaystyle \text{x-intercept: }1$

Correct answer:

$\text{x-intercept: }-1$ $\displaystyle \text{x-intercept: }-1$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2+2x+1$

the coefficients are,

$\\b=2 \\c=1$ $\displaystyle \\b=2 \\c=1$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x+1)(x+1)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x+1=0\rightarrow x=-1$ $\displaystyle \\x+1=0\rightarrow x=-1$

To verify, graph the function.

Screen shot 2016 03 08 at 1.07.18 pm

The graph crosses the $\displaystyle x$-axis at -1, thus verifying the result found by factorization.

Report an Error

Example Question #222 : High School: Algebra

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2+7x+6$

Possible Answers:

$\text{x-intercepts: }6,1$ $\displaystyle \text{x-intercepts: }6,1$

$\text{x-intercepts: }-6,1$ $\displaystyle \text{x-intercepts: }-6,1$

$\text{x-intercepts: }3,2$ $\displaystyle \text{x-intercepts: }3,2$

$\text{x-intercepts: }-6,-1$ $\displaystyle \text{x-intercepts: }-6,-1$

$\text{x-intercepts: }6,-1$ $\displaystyle \text{x-intercepts: }6,-1$

Correct answer:

$\text{x-intercepts: }-6,-1$ $\displaystyle \text{x-intercepts: }-6,-1$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2+7x+6$

the coefficients are,

$\\b=7 \\c=6$ $\displaystyle \\b=7 \\c=6$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x+1)(x+6)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x+1=0\rightarrow x=-1 \\x+6=0\rightarrow x=-6$ $\displaystyle \\x+1=0\rightarrow x=-1 \\x+6=0\rightarrow x=-6$

To verify, graph the function.

Screen shot 2016 03 08 at 1.27.02 pm

The graph crosses the $\displaystyle x$-axis at -6 and -1, thus verifying the results found by factorization.

Report an Error

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2+4x+3$

Possible Answers:

$\text{x-intercepts:}-3,1$ $\displaystyle \text{x-intercepts:}-3,1$

$\text{x-intercepts:}-3,-1$ $\displaystyle \text{x-intercepts:}-3,-1$

$\text{x-intercepts:}-3,-1,1$ $\displaystyle \text{x-intercepts:}-3,-1,1$

$\text{x-intercepts: }3,-1$ $\displaystyle \text{x-intercepts: }3,-1$

$\text{x-intercepts: }3,1$ $\displaystyle \text{x-intercepts: }3,1$

Correct answer:

$\text{x-intercepts:}-3,-1$ $\displaystyle \text{x-intercepts:}-3,-1$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2+4x+3$

the coefficients are,

$\\b=4 \\c=3$ $\displaystyle \\b=4 \\c=3$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x+1)(x+3)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x+1=0\rightarrow x=-1 \\x+3=0\rightarrow x=-3$ $\displaystyle \\x+1=0\rightarrow x=-1 \\x+3=0\rightarrow x=-3$

To verify, graph the function.

Screen shot 2016 03 08 at 1.52.17 pm

The graph crosses the $\displaystyle x$-axis at -1 and -3, thus verifying the results found by factorization.

Report an Error

Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2-2x+1$

Possible Answers:

$\text{x-intercept: }0$ $\displaystyle \text{x-intercept: }0$

$\text{x-intercepts: }0,1$ $\displaystyle \text{x-intercepts: }0,1$

$\text{x-intercepts: }1,-1$ $\displaystyle \text{x-intercepts: }1,-1$

$\text{x-intercept: }-1$ $\displaystyle \text{x-intercept: }-1$

$\text{x-intercept: }1$ $\displaystyle \text{x-intercept: }1$

Correct answer:

$\text{x-intercept: }1$ $\displaystyle \text{x-intercept: }1$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2-2x+1$

the coefficients are,

$\\b=-2 \\c=1$ $\displaystyle \\b=-2 \\c=1$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-1)(x-1)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-1=0\rightarrow x=1$ $\displaystyle \\x-1=0\rightarrow x=1$

To verify, graph the function.

Screen shot 2016 03 09 at 9.54.14 am

The graph crosses the $\displaystyle x$-axis at 1, thus verifying the result found by factorization.

Report an Error

Example Question #7 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2-8x+7$

Possible Answers:

$\text{x-intercepts: }1,8$ $\displaystyle \text{x-intercepts: }1,8$

$\text{x-intercepts: }-1,7$ $\displaystyle \text{x-intercepts: }-1,7$

$\text{x-intercepts: }-1,-7$ $\displaystyle \text{x-intercepts: }-1,-7$

$\text{x-intercepts: }1,7$ $\displaystyle \text{x-intercepts: }1,7$

$\text{x-intercepts: }1,-7$ $\displaystyle \text{x-intercepts: }1,-7$

Correct answer:

$\text{x-intercepts: }1,7$ $\displaystyle \text{x-intercepts: }1,7$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2-8x+7$

the coefficients are,

$\\b=-8 \\c=7$ $\displaystyle \\b=-8 \\c=7$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-1)(x-7)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-1=0\rightarrow x=1 \\x-7=0\rightarrow x=7$ $\displaystyle \\x-1=0\rightarrow x=1 \\x-7=0\rightarrow x=7$

To verify, graph the function.

Screen shot 2016 03 09 at 10.02.27 am

The graph crosses the $\displaystyle x$-axis at 1 and 7, thus verifying the results found by factorization.

Report an Error

Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the $\displaystyle x$-intercept(s) of the function?

$\displaystyle y=x^2-5x+6$

Possible Answers:

$\text{x-intercepts: }2,3$ $\displaystyle \text{x-intercepts: }2,3$

$\text{x-intercepts: }2,-3$ $\displaystyle \text{x-intercepts: }2,-3$

$\text{x-intercepts: }-2,3$ $\displaystyle \text{x-intercepts: }-2,3$

$\text{x-intercepts: }2,1$ $\displaystyle \text{x-intercepts: }2,1$

$\text{x-intercepts: }-2,-3$ $\displaystyle \text{x-intercepts: }-2,-3$

Correct answer:

$\text{x-intercepts: }2,3$ $\displaystyle \text{x-intercepts: }2,3$

Explanation:

One technique that can be used is factorization. In general form,

$y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$ $\displaystyle y=x^2+bx+c\rightarrow(x+c_1)(x+c_2)$

where,

c_1 $\displaystyle c_1$ and c_2 $\displaystyle c_2$ are factors of $\displaystyle c$ and when added together results in $\displaystyle b$.

For the given function,

$\displaystyle y=x^2-5x+6$

the coefficients are,

$\\b=-5 \\c=6$ $\displaystyle \\b=-5 \\c=6$

therefore the factors of $\displaystyle c$ that have a sum of $\displaystyle b$ are,

$\displaystyle y=(x-2)(x-3)$

Now find the $\displaystyle x$-intercepts of the function by setting each binomial equal to zero and solving for $\displaystyle x$.

$\\x-2=0\rightarrow x=2 \\x-3=0\rightarrow x=3$ $\displaystyle \\x-2=0\rightarrow x=2 \\x-3=0\rightarrow x=3$

To verify, graph the function.

Screen shot 2016 03 09 at 10.10.58 am

The graph crosses the $\displaystyle x$-axis at 2 and 3, thus verifying the results found by factorization.

Report an Error

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Common Core: High School - Algebra : Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #1 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #221 : High School: Algebra

Example Question #222 : High School: Algebra

Example Question #2 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #7 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

All Common Core: High School - Algebra Resources

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