Question

Find the x-intercepts of the parabola with

vertex (-4,12) and y-intercept (0,-36).
Write your answer in this form: (x1,Y1),(×2,Y2).
If necessary, round to the nearest hundredth.
the orrect answer

Answer 1

y = a(x + 4)^2 + 12

where "a" is a constant that determines the shape of the parabola. To find the value of "a", we can use the y-intercept (0,-36):

-36 = a(0 + 4)^2 + 12

-36 = 16a + 12

-48 = 16a

a = -3

Therefore, the equation of the parabola is:

y = -3(x + 4)^2 + 12

To find the x-intercepts, we can set y = 0 and solve for x:

0 = -3(x + 4)^2 + 12

3(x + 4)^2 = 12

(x + 4)^2 = 4

x + 4 = ±2

x = -4 ± 2

So the x-intercepts are (-6,0) and (-2,0). Therefore, the answer is:

(-6,0), (-2,0)