Question

Consider the table below.

x    y
-3  0.5
-2  1
-1  2.5
0  5
1  8.5


y=ax2+bx

Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.

Answer 1

y=x^2-6x+13

Explanation:

Answer 2

The standard equation is:
y = ax2 + bx + c
For this case, what we need to do is to evaluate three points in the standard equation and solve the system of three equations with three unknowns.
We have then:
For (-3, 0.5):
0.5 = 9a - 3b + c
For (0, 5):
5 = c
For (1, 8.5):
8.5 = a + b + c
We solve the system:
0.5 = 9a - 3b + c
8.5 = a + b + c
5 = c
From here we get:
a = 1/2
b = 3
c = 5
The standard equation is:
y = (1/2) x ^ 2 + 3x + 5
Answer:
y = (1/2) x ^ 2 + 3x + 5