Find an equation in the form y=ax^2+bx+c for the parabola passing through the points. (-4,94)(3,24)(-2,34)

Answer 1

The graph of the parabola passes through (-4,94) which means when x = -4, y = 94.

16a - 4b + c = 94.

Similarly for the other two points:

9a + 3b + c = 24

4a - 2b + c = 34

So this resulted in a system of 3 equations with 3 unknowns.

Probably the easiest way to solve this system is using addition/elimination.

The variable c is the easiest to eliminate first. Subtract the 2nd equation from the first:

7a - 7b = 70 => a - b = 10

Subtract the 3rd equation from the 2nd:

5a + 5b = -10 => a + b = -2

By adding those last two equations, b is eliminated:

2a = 8

a = 4.

If a = 4, then b = -6.

This means (using the 3rd equation containing a, b, c:

4(4) - 2(-6) + c = 34

c = 6.

So the equation of the parabola containing the given points is:

y = 4x² - 6x + 6

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