Find the quadratic polynomial whose graph goes through the points

Question

Find the quadratic polynomial whose graph goes through the points (-2,10) (0,6) (1,13)

f(x)=__x^2+__x+__

i know the we substitute x and you to the equation and we get that c=6 but what do we do after?

Answer 1

f(x) = Ax² + Bx + C

Since (0,6) is on the graph, f(0) = 6. So, C = 6.

So, f(x) = Ax² + Bx + 6

Since (-2,10) and (1,13) are on the graph, f(-2) = 10 and f(1) = 13

So, 4A - 2B = 4 and A + B = 7

Divide the first equation by 2 and get:

2A - B = 2

A + B = 7

Adding the equations gives 3A = 9. So, A = 3 and B = 4.

Therefore, f(x) = 3x² + 4x + 6