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Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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

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

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

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

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

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

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

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Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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

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

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

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

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

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

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

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Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

Explanation:

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.

Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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

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

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

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

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

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

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

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Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

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.

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Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

All Common Core: High School - Algebra Resources

Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

Flashcards: Identify Zeros, Factor and Graph Polynomials: CCSS.Math.Content.HSA-APR.B.3

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