6.100 - Intermediate Algebra

Question

For the function $f\left(x\right)=x^2-8x+3$

(a) find $x$ when $f\left(x\right)=-4$

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

Step-by-Step Solution

Answer

The value of $x$ is $1,7$ and points lying on the graph is $(1,-4),(0,3)$

Step 1: Given information

Given the function $f\left(x\right)=x^2-8x+3$

Step 2: Substitute, f ( x ) = - 4 and calculate the value

Substituting the values, we get

$$\begin{gathered} -4=x^2-8x+3 \\ {x}^2-8x+7=0 \\ {x}^2-7x-x+7=0 \\ x(x-7)-1(x-7)=0 \\ (x-1)(x-7)=0 \\ x=1,7 \end{gathered}$$

Step 3: Calculate the corresponding y values

The corresponding points that lie on the graph is $(1,-4),(0,3)$ the graph of which is