187k views
2 votes
Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)

User Krvolok
by
8.6k points

1 Answer

3 votes
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
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories