Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
