Question

The minimum of a parabola is located at (–1, –3). The point (2, 20) is also on the graph. Which function represents the situation

Answer 1

Answer:

       23
y = ----- (x + 1)^2 - 3
        9

Explanation:

Use the general vertex form equation of the parabola to find the function.

1) Vertex form equation: y = A (x - h)^2 + k

Where h and k are the vertex - coordinates, i.e. vertex = (h,k)

2) The vertex is the minimum (or maximum) of the parabola. In this case it is (-1,-3)

=> h = -1, k = -3.

3) Replace the vertex-coordinates in the vertex form equation of the parabola:

y = A(x + 1)^2 - 3

4) To find A replace the coordinates of the other point given: (2,20)

=> 20 = A(2 + 1)^2 - 3

=> A(3^2) = 20 + 3

=> A(9) = 23

=> A = 23/9

5) Replace h, k and A in the vertex form of the parabola:

y = (23/9) (x + 1)^2 - 3