Question

What is the equation, in standard form, of a parabola that contains the following points?(–2, –20), (0, –4), (4, –20)

Answer 1

@Hero or @Preetha can one of you help me?

Answer 2

How do you do that?

Answer 3

how do you solve for a? sorry, still getting the hang of this

Answer 4

I think you may have to start with the general equation of a parabola:
y = ax^2 + bx + c
Substitute the three points: (–2, –20), (0, –4), (4, –20) into the equation and solve for a, b and c.

Answer 5

The middle point right away gives c = -4

Answer 6

The vertex for this parabola happens to be at (1, -2).

Answer 7

I am getting y = -2x^2 + 4x - 4

Answer 8

Can one of you walk me through this?

Answer 9

y = ax^2 + bx + c
Substitute (–2, –20), (0, –4), (4, –20).
First try the middle point. when x = 0, y = -4
-4 = 0 + 0 + c. c = -4
y = ax^2 + bx - 4
put x = -2, y = -20
-20 = 4a - 2b - 4
-16 = 4a - 2b
-8 = 2a - b
2a - b = -8 ---- equation (1)
put x = 4, y = -20
-20 = 16a + 4b - 4
-16 = 16a + 4b
-4 = 4a + b
4a + b = -4 ---- equation (2)
Add equations (1) and (2):
6a = -12
a = -2
Put a = -2 in equation (1):
2(-2) - b = -8
-4 - b = -8
b = 4

Therefore, y = -2x^2 + 4x - 4