Question

How to write the vertex form of a quadration that has the vertex of (3,3) and passes through the point (5,11)?

Answer 1

"quadration?"  "quadratic equation?"

Write out the general vertex form and then plug in the given info:

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

Vertex at (3,3):     y = a(x-3)^2 + 3

curve passes thru (5,11):    11 = a(5-3)^2 + 3
                                            11 = a(2)^2 + 3 = 4a + 3 = 11, or a = 2
                             
                                             Then the equation of this parabola is

                                             y = 2(x-3)^2 + 3.

check:  Does this pass thru (5,11)?   Is  11 = 2(5-3)^2 + 3 true?
                                                           Is  11 = 2(4)+3 true?  YES