Question

The graph of f(x) and table for g(x) = f(kx) are given.

The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.


x g(x)
−8 8
−4 2
0 0
4 2
8 8

What is the value of k?
k is equal to one fifth
k = 5
k is equal to one fourth
k = 4

Answer 1

Answer: C. k is equal to one fourth

Explanation:

formula for parabola in vertex form

y= a(x-h)²+k (h, k) is vertex here it is (0,0)

f(x)=ax² another point we can plug in is (1,2)

2=a1

a= 2

so f(x)= 2x²

g(x)= f(kx) plug in kx into f(x)

g(x) = 2(kx)²

g(x) = 2(k²)(x²) plug in a point and find k (4,2)

2 = 2 k²4²

k²=1/16

k=1/4

C