Question

How do you find the quadratic function with vertex (5/2, -3/4) and point (-2,4)?

Answer 1

`f(x) = (19/81)(x - 5/2)^2 - 3/4`

Explanation:

Vertex form of this function:
`f(x) = a(x - 5/2)^2 - 3/4`
To find a, write that this parabola passes at point (- 2, 4)
`f(x) = 4 = a (-2 - 5/2)^2 - 3/4 = (a/4)(2x - 5)^2 - 3/4`
`f(x) = (81a)/4 - 3/4 = 4`
81a = 19 --> `a = 19/81`
Equation of y:
`f(x) = (19/81)(x - 5/2)^2 - 3/4`