Question

What is the equation of a parabola with vertex (-8, – 7) that passes through (-7, -9)?

A) y = -2(x + 8)^2 - 7
B) y = -2(x + 7)^2 - 9
C) y = -2(x + 8)^2 - 9
D) y = -2(x + 7)^2 - 7

Answer 1

By using the vertex form of a parabola and the given vertex (-8, -7), along with a point (-7, -9) that the parabola passes through, we find that the correct equation is y = -2(x + 8)^2 - 7.

Step-by-step explanation:

The equation of a parabola is generally represented in vertex form as y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. Given the vertex (-8, -7), we substitute h with -8 and k with -7, leading to the form y = a(x + 8)^2 - 7.

To find the value of 'a', we use the point (-7, -9) which lies on the parabola. Substituting these values into the vertex form gives us -9 = a(-7 + 8)^2 - 7. Simplifying leads to -2 = a, which gives us the final equation of the parabola as y = -2(x + 8)^2 - 7.

Therefore, the correct answer is A) y = -2(x + 8)^2 - 7.