How do I find the equation in standard form of the parabola passing through the points (1,-2) (2,-2) (3,-4)?

Question

I tried figuring it out but ended up getting c = 26 and a = -32

i feel like I’m doing this wrong...any help?

Answer 1

Forunately, the numbers are not too terrible.

Ax² + Bx + C = y

A + B + C = -2

4A + 2B + C = -2

9A + 3B + C = -4

You know immediately that the vertex is at a x=1/2 bu that really doesn't help you much

Anyway, subtract the first equation from the 2nd and 3rd to get

3A + B = 0

8A + 2B = -2

B=-3A

Substitute

8A - 6A=-2

You solve it from here.