first, write the equation of the parabola in the required form:
(y - k) = a·(x - h)²
Here, (h, k) is given as (-1, -16).
So you have:
(y + 16) = a · (x + 1)²
Unfortunately, a is not given. However, you do know one additional point on the parabola: (0, -15):
-15 + 16 = a· (0 + 1)²
.·. a = 1
.·. the equation of the parabola in vertex form is
y + 16 = (x + 1)²
The x-intercepts are the values of x that make y = 0. So, let y = 0:
0 + 16 = (x + 1)²
16 = (x + 1)²
We are trying to solve for x, so take the square root of both sides - but be CAREFUL!
± 4 = x + 1 ...... remember both the positive and negative roots of 16......
Solving for x:
x = -1 + 4, x = -1 - 4
x = 3, x = -5.
Or, if you prefer, (3, 0), (-5, 0).
