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?
number of x intercepts in this equation is 2 because max power in the function is 2. number of x intercepts is determined by "highest power".
let x1 represent first x intercept and
let x2 represent second x intercept
Formula for finding average of x intercepts is logicaly:
Avg = (x1 + x2)/2
we want to find x1 and x2
4x^2 - 24x + 20 = 0
x^2 - 6x + 5 = 0
\(x = \frac{6 +- \sqrt{6^2 - 4*1*5} }{2*1}\)
x1 = 5
x2 = 1
Avg = 3