Question

For the function f(x) = x^2 – 8x + 8, use f(x) = -4 to find two points on the graph of the function. (__,__) , (__,__)

Answer 1

(2, -4) and (6, -4)

Step-by-step explanation

We are given the function:

`f(x)=x^2\text{ - 8x + 8}`

We want to find the value of x such that f(x) = -4. The solution will be written in the form (x, f(x))

We have that:

`\begin{gathered} f(x)=x^2\text{ - 8x + 8 = -4} \\ \Rightarrow x^2\text{ - 8x + 8 + 4 = 0} \\ \Rightarrow x^2\text{ - 8x + 12 = 0} \\ \text{Factorising:} \\ x^2\text{ - 2x - 6x + 12 = 0 } \\ x(x\text{ - 2) - 6(x - 2) = 0} \\ (x\text{ - 2)(x - 6) = 0} \\ \Rightarrow\text{ x = 2 and x = 6} \end{gathered}`

Therefore, the two points are:

(2, -4) and (6, -4)