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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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

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,

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

where,

$\displaystyle c_1$ and $\displaystyle c_2$ 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,

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

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 $\displaystyle x$.

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

To verify, graph the function.

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