Make a quadratic equation using points (0,-5), (2,13), (-3, -62)?

A quadratic equation is y = ax^2 + bx + c

You are given three variables and you are given three sets of values, so this is just a simple simultaneous system.

First point: (0,-5)
-5 = c

Second point: (2,13)
13 = 4a + 2b - 5

Third point: (-3, -62)
-62 = 9a - 3b - 5 Let's work with this one. Add 5.
-57 = 9a - 3b Add 3b.
3b - 57 = 9a Divide by 3.
b - 19 = 3a Add 19.
b = 3a + 19 Substitute this for b in eqn #2.

13 = 4a + 2(3a + 19) - 5
13 = 4a + 6a + 38 - 5
13 = 10a + 33 Subtract 13.
0 = 10a + 20 Divide by 10.
0 = a + 2 Subtract 2.
a = -2