Q 6.99 - Intermediate Algebra

Question

For the function $f\left(x\right)=x^2-2x-8$

(a) find $x$ when $f\left(x\right)=7$

(b) Find two points that lie on the graph of the function.

Step-by-Step Solution

Answer

The value of $x$ is $-3,5$ and the points lying on the graph is $(0,-8),(1,-9)$

Step 1: Given information

Given the equation $f\left(x\right)=x^2-2x-8$

Step 2: Substitute f ( x ) = 7 and calculate the value

Substituting the value, we get

$$\begin{gathered} 7=x^2-2x-8 \\ {x}^2-2x-15=0 \\ {x}^2-5x+3x-15=0 \\ x(x-5)+3(x-5)=0 \\ (x+3)(x-5)=0 \\ x=-3,5 \end{gathered}$$

Step 3: Calculate the corresponding y values

The values are $(0,-8),(1,-9)$ the graph of which is