MATH SOLVE

5 months ago

Q:
# The vertex of this parabola is at (-5,-2). when the x-value is -4, the y-value is 2. what is the coefficient of the squared expression in the parabola's equation

Accepted Solution

A:

Vertex: (-5,-2); parabola opens up;

General form of the equation for a vertical parabola opening up is:

y-k = a(x-h)^2; knowing that the vertex is at (-5,-2), we can write:

y+2 = a(x+5)^2. We need to find the value of the coefficient a.

From the graph we see that y is 10 when x is approx. -1 3/4 (or -7/4).

subst. these values into y+2 = a(x+5)^2, we get:

10 + 2 = a(-7/4 + 5)^2, or 12 = a(13/4)^2, or 1 = a(169/16).

Solving for a: a = 16/169 = 0.09, or approx 16/160, or 1/10. Unfortunately, this is not close to any of the four answer choices.

I thought it best to try again, and fortunately my second try was correct:

10+2 = a(13/4)^2, or (169/16)a. Thus, 12 = a(169/16)

12

Solving for a: a = ------------- = 1.14. The answer choice closest to this is 1.

169/16

Answer A is correct.

General form of the equation for a vertical parabola opening up is:

y-k = a(x-h)^2; knowing that the vertex is at (-5,-2), we can write:

y+2 = a(x+5)^2. We need to find the value of the coefficient a.

From the graph we see that y is 10 when x is approx. -1 3/4 (or -7/4).

subst. these values into y+2 = a(x+5)^2, we get:

10 + 2 = a(-7/4 + 5)^2, or 12 = a(13/4)^2, or 1 = a(169/16).

Solving for a: a = 16/169 = 0.09, or approx 16/160, or 1/10. Unfortunately, this is not close to any of the four answer choices.

I thought it best to try again, and fortunately my second try was correct:

10+2 = a(13/4)^2, or (169/16)a. Thus, 12 = a(169/16)

12

Solving for a: a = ------------- = 1.14. The answer choice closest to this is 1.

169/16

Answer A is correct.