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 $f(x) = 4x^2 - 24x + 20$?
\\(\frac{-5 - 1}{2} = -3\\)
\\(\frac{-10 - 2}{2} = -4\\)
\\(\frac{1 + 5}{2} = 3\\)
\\(\frac{2 + 10}{2} = 4\\)

Explanation:

Step1: Find x-intercepts (set f(x)=0)

Set \( 4x^2 - 24x + 20 = 0 \). Divide by 4: \( x^2 - 6x + 5 = 0 \).

Step2: Factor the quadratic

Factor \( x^2 - 6x + 5 \): \( (x - 1)(x - 5) = 0 \). So roots are \( x = 1 \) and \( x = 5 \).

Step3: Calculate the average

Average of 1 and 5: \( \frac{1 + 5}{2} = 3 \).

Answer:

\(\boldsymbol{\frac{1 + 5}{2} = 3}\) (the third option: \(\frac{1 + 5}{2} = 3\))