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Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)

User Krvolok
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1 Answer

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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).
User KingKerosin
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