Question

the vertex of the parabola is (-3,5) and is the minimum point of the graph. If the graph passes though the pont (-2,7) what is the equation of the quadra tic form?

Answer 1

The equation of the parabola with vertex (-3,5) and passing through the point (-2,7) is y = 2(x + 3)^2 + 5.

Step-by-step explanation:

The student is asking for the equation of a parabola with its vertex at (-3,5) and a given point (-2,7) that it also passes through.

Since the vertex is a minimum point, we can use the vertex form of the parabolic equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Here, h = -3 and k = 5, giving us the initial form of y = a(x + 3)^2 + 5.

To find the value of a, we use the point (-2,7) which yields the equation 7 = a(-2 + 3)^2 + 5.

Solving this, we get 7 = a(1)^2 + 5 which simplifies to a = 2.

Therefore, the equation of the parabola is y = 2(x + 3)^2 + 5.