Question

Instructions: Given the quadratic function, find the -value of the vertex (axis of symmetry).

Answer 1

Answer

x = 4

Explanation

Given:

The given quadratic equation is

$y=x^2-8x-2$

What to find:

To find the x-value of the vertex of the quadratic equation.

Step-by-step solution:

The solution involves two steps.

Step 1: Find the value of y at maximum (y-max)

The formula to get y-max is given by

$y(max)=c-\frac{b^2}{4a}$

From the quadratic equation given, a = 1, b = -8 and c = -2

Therefore

$y(max)=-2-\frac{(-8)^2}{4\times1}=-2-\frac{64}{4}=-2-16=-18$

y-max = -18

Step 2: Determine x-vale at y-max.

$\begin{gathered} -18=x^2-8x-2 \\ \\ x^2-8x-2+18=0 \\ \\ x^2-8x+16=0 \\ \\ By\text{ }factorization \\ \\ x^2-4x-4x+16=0 \\ \\ x(x-4)-4(x-4)=0 \\ \\ (x-4)(x-4)=0 \\ \\ x-4=0,x-4=0 \\ x=4 \end{gathered}$

The x-value of the vertex is 4