Question

What is the equation, in standard form, of a parabola that contains the following points? (-2,18),(0,4),(4,24)

Answer 1

y=ax² + bx + c and A(-2,18), B(0.4), C(4,24) given

1)Let's determine 1st the value of c in using the pair of B
4= a(0)² + b(0) + c , c=4 and y=ax²+bx+4

2) Use the pair of A: 18 = 4a -2b + 4===> 4a-2b=14

3) Use C pair: 24 = 16a+4b+4 ==> 16a+4b=20

4) solve the system equation in 2) and 3) and you'll find a=2 and b=-3

Hence the equation is y =2x²-3x+4