Question

What is the equation, in standard form, of a parabola that models the values in the table?
x= -2, 0, 4
f(x)= 0, -6, 78

Answer 1

f(x) is the same meaning as y.

Answer 2

yes and it is called function of x

Answer 3

I think you start out
f(-2)=4a+(-2b)+3=0
f(0)=ax^2+bx+c=-6 c=-6
f(4)=16a+4b+3=78

Answer 4

Yes, sortof. You'll need to solve a system of two linear equations.

Answer 5

You also have x- and y-intercepts, which makes it much easier.

Answer 6

Start with the standard form template:

f(x)=ax^2+bx+c

Then put in your known values:

f(-2) = a(-2)^2+b(-2)+c = 0
f(0) = a(0)^2+b(0)+c = -6
f(4) = a(4)^2+b(4)+c = 78

From the second equation, you can see that c = -6, so you can substitute that back in the other two.

Answer 7

You have the right idea, just be careful about how you write the equations.