Given three points, find the equation of a parabola.?

Question

Given the following points:

(50, -9796)
(5.5, -95)
(-7, -220)

Find the equation of the parabola.

Answer 1

The general equation of a parabola is y = ax^2 + bx + c

You have three pairs of points that are (x,y) ordered pairs. Substitute the x and y values of each point into the equation for a parabola. You will get three LINEAR equations in three unknowns, the three constants.
You can then solve this system of three equations for the values
of A, B, and C, and you'll have the equation of the parabola that
intersects your 3 points.

Answer 2

Seeing that it passes through (4,0) and (-2,0), you have both of the zeros of the function. If you have two zeros of a parabola, you can subtract each of those from x, multiply those together, and multiply by a to get your whole equation. y = a(x-4)(x - -2) y = a(x-4)(x+2) y = a(x^2 + 2x - 4x - 8) y = a(x^2 - 2x - 8) Now, we need to find a, and we'll be all done. Plug in the other point that we know, (1,12): 12 = a(1^2 - 2(1) - 8) 12 = a(1 - 2 - 8) 12 = a(-9) 12 = -9a -4/3 = a So we now have: y = (-4/3)(x^2 - 2x - 8)

Answer 3

I thought you give me 10 points if I get it :-)

ax^2 + bx + c = y
Plug in:

2500a + 50b + c = -9796
30.25a + 5.5b + c = -95 (or 121a + 22b + 4c = -380)
49a - 7b + c = -220

Then solve these equations to get the solution

Answer 4

a*(50)^2+b(50)+c=-9796
a*(5.5)^2+b(5.5)+c=-95
a(-7)^2+b(-7)+c=-220
Now solve this system to get the coefficients a, b, c.