Equation of parabola in Vertex form

Question

Write the equation of the parabola in vertex form. vertex (2,2), point (3,-3)

Answer 1

From Wikipedia:
"A univariate quadratic function can be expressed in three formats:
  f(x) = ax² + bx +c   is called the standard form,
  f(x) = (x-x1)(x-x2)    is called the factored form, where x1 and x2 are the roots of the quadratic function and the solutions of the corresponding quadratic equation.
  f(x) = a(x-h)² + k    is called the vertex form, where h and k are the x and y coordinates of the vertex, respectively."

 

The problem gives us: h=2, k=2 and point (3,-3) is on the curve:

   Let's find the value of (a) using the point (3,-3):

        f(x) = a(x-h)² + k

        -3 = a(3-2)² + (2)

        -3 = a(1) + 2

        -5 = a

 

The equation is    f(x)=  (-5)(x-2)² + 2