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? 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

Answer 1

it's C in edge

Explanation:

I just took the test

Answer 2

`\bf \displaystyle(5+1)/(2)=\displaystyle(6)/(2)=3`

Explanation:

The x-intercepts are the values of x for which y=0, that is f(x)=0.

The x-intercepts of

`\bf f(x)=4x^2-24x+20`

are the values of x such that

`\bf 4x^2-24x+20=0`

Divide both sides by 4 to simplify a little

`\bf x^2-6x+5=0`

Solve the quadratic equation

`\bf x=\displaystyle(-(-6)\pm√((-6)^2-4*1*5))/(2*1)=\displaystyle(6\pm√(36-20))/(2)=\\\\=\displaystyle(6\pm√(16))/(2)=\displaystyle(6\pm4)/(2)`

and you get the 2 x-intercepts

x =10/2 and x = 2/2

or

x = 5 and x = 1

The average is the midpoint

`\bf \displaystyle(5+1)/(2)=\displaystyle(6)/(2)=3`