Question

Find the x intercept

Answer 1

Answer:

the x-intercepts are (5, 0) and (-3, 0).

Step-by-step explanation:

The standard equation of a vertical parabola with vertex at (h, k) is

y = a(x - h)^2 + k.  

Here we are told that the vertex is at (1, -16), which means that h = 1 and y = -16.  Thus, we have:

y = a(x - 1)^2 + (-16).

We are told also that the graph passes through (0, -15).  Substituting -15 for y and 0 for x, we get:

-15 = a(0 - 1)^2 - 16, or

-15 = a - 16

Then a must be 1, and the equation of the parabola is

y = (x - 1)^2 - 16.

Now to find the x-intercepts:  Set y = 0 and solve for x:

0 = (x - 1)^2 - 16, or

(x - 1)^2 = 16, or

x - 1       = ±√16 = ±4

Then x = 1 ± 4, or x = 5 or x = -3, so the x-intercepts are (5, 0) and (-3, 0).