Question

PLEASE HELP I NEED HELP ASAP PLEASE

Use the information given to write the equation for the quadratic function.
a. The x-intercepts are (-4, 0) and (3,0), and the parabola opens down.
b. The vertex is (-8, -2), and the parabola opens up.

Answer 1

y = -x² - x/22 + 6/11

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!