What is the equation of g(x) if the parent function is f(x) = x^2 and a = 2, h = -5 and k = 7

Question

f(x) = 2(x-5)^2 + 7
F(x) = -3(x+5)^2 + 7
f(x) = 2(x+5)^2 + 7
f(x) = 2(x-5)^2 -7

I think it is 2(x+5)^2 + 7, is that right

Answer 1

Yes, if you are aiming for the general quadratic in the form
f(x) = a(x-h)^2 + k

Answer 2

Since you do not defined what a, h and k are in terms of any function, I have no idea.

Answer 3

Thanks Reiny. I had never seen that general form before

Answer 4

Some authors call it the "standard" form of a parabola, it displays the vertex (h,k).
A second point on the graph is needed to find a.

Answer 5

Thanks Reiny-I really appreciate it-I get confused about taking the "h" at times

So if they say h= (-5), then in the equation when it is written,it is positive and vice-versa, correct?

Answer 6

correct, since in the formula you have
...(x-h)^2 ....

for x-(-5) it would become x+5
for x-(+5) it would become x-5

Answer 7

Thanks alot-At least I get one concept!