Question

what is the vertex of the function? f(x)=(x - 1)(x + 7) (-3,-16) (0,-7) (-6,-7) (3,20)

Explanation:

Step1: Expand the function

\[

$$\begin{align*} f(x)&=(x - 1)(x+7)\\ &=x^{2}+7x - x-7\\ &=x^{2}+6x - 7 \end{align*}$$

\]

Step2: Use the vertex - formula for a quadratic function

For a quadratic function \(y = ax^{2}+bx + c\), the x - coordinate of the vertex is \(x=-\frac{b}{2a}\). Here \(a = 1\), \(b = 6\), so \(x=-\frac{6}{2\times1}=- 3\).

Step3: Find the y - coordinate of the vertex

Substitute \(x=-3\) into \(y=x^{2}+6x - 7\). Then \(y=(-3)^{2}+6\times(-3)-7=9 - 18 - 7=-16\).

Answer:

(-3, - 16)