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

Answer:

$\bf \displaystyle\frac{5+1}{2}=\displaystyle\frac{6}{2}=3$

Step-by-step 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

$\bf x=\displaystyle\frac{-(-6)\pm\sqrt{(-6)^2-4*1*5}}{2*1}=\displaystyle\frac{6\pm\sqrt{36-20}}{2}=\\\\=\displaystyle\frac{6\pm\sqrt{16}}{2}=\displaystyle\frac{6\pm4}{2}$

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

$\bf \displaystyle\frac{5+1}{2}=\displaystyle\frac{6}{2}=3$

Answer 2

Answer:

it's C in edge

Step-by-step explanation:

I just took the test