Question

Apex A parabola opens upward. The parabola goes through the point (3,-1), and the vertex (2,-2). What are the values of hand v? (2 point)

Answer 1

Since the parabola opens upward, the standard form of the equation for the parabola is:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We know that the vertex of the parabola is (2, -2), so we have:

y = a(x - 2)^2 - 2

We also know that the parabola goes through the point (3, -1), so we can substitute these coordinates into the equation and solve for a:

-1 = a(3 - 2)^2 - 2
-1 = a - 2
a = 1

Therefore, the equation of the parabola is:

y = (x - 2)^2 - 2

The values of h and v are the coordinates of the vertex, which we already know to be (2, -2). Therefore, h = 2 and v = -2