Question

Find a quadratic function that includes the set of values below.

Answer 1

Plug in points to general form of quadratic function:
y=ax²+bx+c

(0,7)
7 = c
(2,13)
13 = 4a +2b + c
(4,3)
3 = 16a + 4b + c

Now solve the system of equations in two unknowns.

Substitute the value of 7 for c in the second equation:
13 = 4a + 2b + 7
6 = 4a + 2b
3 = 2a + b
b = 3 - 2a

Substitute this into third equation:
3 = 16a + 4(3-2a) + 7
3 = 16a + 12 - 8a + 7
3 = 8a + 19
-16 = 8a
a = -2

b = 3-2a = 3 - 2(-2) = 7

a = -2, b =7. c = 7
The quadratic function is y= -2x² + 7x +7