Q. 437 - Intermediate Algebra

Question

For the function, $f\left(x\right)=x^2+11x+20$, (a) find

when $f\left(x\right)=-8$ .(b) Use this information to find two

points that lie on the graph of the function.

Step-by-Step Solution

Answer

(a) The $x$ values for $f\left(x\right)=-8$ are $x=-7,-4$

(b) Two points that lie on the graph of function are $(-7,-8),(-4,-8)$

Step 1. Given

The function is $f\left(x\right)=x^2+11x+20$

(a) We have to find when $f\left(x\right)=-8$

(b) We also have to find two points that lie on the graph of the function.

Step 2. Find values of x when f ( x ) = - 8

$$\begin{gathered} f\left(x\right)=x^2+11x+20 \\ -8=x^2+11x+20 \\ {x}^2+11x+28=0 \\ {x}^2+7x+4x+28=0 \\ x(x+7)+4(x+7)=0 \\ (x+7)(x+4)=0 \end{gathered}$$

So,

$x=-7,-4$

Step 3. Check the value of f ( x ) at x = - 7 , - 4

Substitute $x=-7$ in $f\left(x\right)$,

data-custom-editor="chemistry" $$\begin{gathered} f\left(x\right)=x^2+11x+20 \\ \mathrm{f}(-7)={(-7)}^2+11(-7)+20 \\ \mathrm{f}(-7)=49-77+20 \\ \mathrm{f}(-7)=-8 \end{gathered}$$

Substitute $x=-4$ in $f\left(x\right)$

$$\begin{gathered} f\left(x\right)=x^2+11x+20 \\ f(-4)={(-4)}^2+11(-4)+20 \\ f(-4)=16-44+20 \\ f(-4)=-8 \end{gathered}$$

Step 4. Find two points that lie on the graph of the function.

Since, $f(-7)=-8$ and $f(-4)=-8$, so the points $(-7,-8)$ and $(-4,-8)$ lie on the graph of the function.