Question

What is the equation, in standard form, of a parabola that contains the following points?
(-2,-20),(0,-4),(4,-20)

Answer 1

What an interesting question!
The equation in standard form of a parabola is y = a*x^2 + b*x + c (the ' * ' indicates multiplication).
We are given 3 separate points that must lie on the same graph of the same parabola.
for example, (-2,-20) tells us that when x = -2, y = -20.
Starting with y = a*x^2 + b*x + c, substitute the x and y value from each of the given three points. You'll end up with three equations in three unknowns.

Once you've done that, consider how you'd solve the resulting system for the coefficients a, b and c.

Answer 2

So I would have
-20=a(-2)^2+b(-2)+c
-4=a(0)^2+b(0)+c
-20=a(4)^2+b(4)+c

Answer 3

@mathmale

Answer 4

Looks like you're right on target!! I'm not going to check your arithmetic, but will assume that it's correct.
Then you'd have 4a - 2b + c = -20 from the first of your equations;
c = -4 from the second; and
16a + 4b + c = -20 from the third.

Are you familiar with any of the usual methods of solving systems of linear equations?
There's addition/subtraction, substitution, graphing, determinants, Cramer's Rule, matrices, and so on.

I'd suggest you take advantage of knowing that c = -4 and substitute that value for "c" in each of the other two equations. Then:
4a - 2B =-16
16a + 4b = -16

I used my calculator (and matrices) to solve this system. My results: a = -2, b = 4, c = -4.

Write out the polynomial using these a, b and c values.
Then check any of the 3 given points by substituting the x- and y-coordinates.
Is the resulting equation true? If so, we have the correct values for a, b and c.

Answer 5

Ask if you'd like help and/or practice in solving systems of linear equations.