Question

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?

Answer 1

There can only be two definite x-intercepts, so your goal it to find 2 numbers of x that, when plugged into the equation, give you the answer of 0. 1 is the first x-intercept(4-24+20 equals 0). The second one is 5 (100-120+20 equals 0). So the average is 3, so the axis of symmetry is 3 since 5+1=6, and 6/2=3

Honestly, there is an easier way to find the axis of symmetry. the equation would be -b/2a, where as b is the coefficient in the second part of the equation, while a is the first coefficient in the equation. -(-24) is 24, and 4*2=8, so 24/8=3

I hope I actually answered this the way you wanted. You asked for an equation, but I just answered the axis of symmetry with very simple equation initially and another equation

Answer 2

To get the x-intercepts of the function, f(x) = 4x2 – 24x + 20

It has to be equated to zero and the values of x are the x-intercepts. So,

4x2 – 24x + 20 = 0

The resulting equation is a quadratic equation which can be solved by different methods. The solution is

x = 5, 1

The average therefore is:

(1+5/)2 = 3