Answer:
y = -x² - x/22 + 6/11
Step-by-step explanation:
Standard form, is y = ax² + bx + c
We need to use standard form (though we could use vertex form, but it is easier to do standard form)
Substitute the x and y values that they give into y = ax² + bx + c
Because the parabola passes through...
(-4, 0), then 0 = (-4)²a + (-4)b + c
(3, 0), then 0 = 9a + 3b + c
(-8, -2), then -2 = 64a - 8b + c
So, we get this system:
16a − 4b + c = 0
9a + 3b + c = 0
64a − 8b + c = −2
Because you are learning about parabolas, I am assuming that you can solve a system, but the answers are:
a = -x²/22
b = -x/22
c = 6/11
So, the equation of the parabola is:
y = -x²/22 - x/22 + 6/11
I hope this helps! Feel free to ask any questions!
