Question

Find the equation, in standard form, of the parabola going through (-2,4),(0,-4), and (2,4). What is a + b + c?. There is no visual. I NEED THIS ASAP

Answer 1

• y = 2x^2 - 4

• a + b + c = -2

Explanation:

Parabola is the graph of a quadratic function:

• y = ax^2 + bx + c

Given points:

• (-2,4), (0,-4) and (2,4)

Substituting the points:

1.

• 4 = a(-2)^2 + b(-2) + c ⇒ 4 = 4a - 2b + c ⇒ 4a -2b + c = 4

2.

• -4 = a*0 + b*0 + c ⇒ c = -4

3.

• 4 = a(2)^2 + b(2) + c ⇒ 4 = 4a + 2b + c ⇒ 4a + 2b + c = 4

Considering c = -4 in the other equations:

• 4a - 2b - 4 = 4 ⇒ 4a - 2b = 8

and

• 4a + 2b - 4 = 4 ⇒ 4a + 2b = 8

Comparing the above two equations:

• 4a - 2b = 4a + 2b ⇒ 4b = 0 ⇒ b = 0

Then finding a:

• 4a = 8 ⇒ a = 2

So we have equation:

• y = 2x^2 - 4

and

• a + b + c = 2 + 0 - 4 = -2