William W. answered • 02/21/19

Experienced Tutor and Retired Engineer

The standard form of a quadratic equation is y = ax^{2} + bx + c so plug in each of the given points to get an equation. To plug in the first point, (1, 7), plug in x = 1 and y = 7 into y = ax^{2} + bx + c to get 7 = a(1)^{2} + b(1) + c or:

a + b + c = 7

To plug in the second point, (2, 2), plug in x = 2 and y = 2 into y = ax^{2} + bx + c to get 2 = a(2)^{2} + b(2) + c or:

4a + 2b + c = 2

To plug in the third point, (4, -32), plug in x = 4 and y = -32 into y = ax^{2} + bx + c to get -32 = a(4)^{2} + b(4) + c or:

16a + 4b + c = -32

Now you have three equations in three unknowns that you can solve using either substitution or elimination (or your preferred method). (If you'd like help with thi, let me know.)

Solving gives you a = -4, b = 7, and c = 4

So the equation is y = -4x^{2} + 7x + 4