Question

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

Answer 1

x = 4

Step-by-step 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-(b^2)/(4a)`

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

Therefore

`y(max)=-2-((-8)^2)/(4*1)=-2-(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