What is the equation of a parabola that passes through the following points (2, −8), (3, −8), (6, 4)? To find a, b, and c, use the 3 equation solver:

Question

What is the equation of a parabola that passes through the following points

            (2, −8), (3, −8), (6, 4)?

                To find a, b, and c, use the 3 equation solver: 

Answer 1

(6,4),(2,-8), (3,-8)

it's an upward opening vertical parabola with x coordinate of the vertex = 2 1/2 =2.5 = 5/2

midway between 2 and 3. It helps to plot the points.

y = a(x-5/2)^2 + k where a>0 and k<-8

4 = a(6-2.5)^2+k

-8=a(2-2.5)^2+k

subtract

12=a(12.25 - .25)

a = 1

4=(3.5)^2 + k

k = 4-12.25= -8.25

y=(x-2.5)^2 - 8.25

or if you didn't realize you could easily calculate the vertex' x coordinate, then

go with 3 equations if you prefer

y =ax^2 +bx +c

plug in the 3 points and get 3 equations, 3 unknowns and solve by elimination, substitution or matrix algebra

-8 = 4a +2b +c

-8 = 9a +3b +c

4 = 36a +6b + c