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?
StartFraction negative 5 minus 1 Over 2 EndFraction = negative 3 = –3
StartFraction negative 10 minus 2 Over 2 EndFraction = negative 4 = –4
StartFraction 1 + 5 Over 2 EndFraction = 3 = 3
StartFraction 2 + 10 Over 2 EndFraction = 4 = 4
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Given : f(x) = 4x² – 24x + 20 average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis
To find : Which equation represents the average of the x-intercepts for f(x)
Solution:
f(x) = 4x² – 24x + 20
4x² – 24x + 20 = 0
=> x² - 6x + 5 = 0
=> x² - x - 5x + 5 = 0
=> x(x - 1) - 5(x - 1) = 0
=>(x - 5)(x - 1) = 0
=> x= 5 or x = 1
=> x average = (5 + 1)/2 = 3
x = 3
(1 + 5)/2 = 3 Represent the average of the x-intercepts for f(x) = 4x² – 24x + 20
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