What is the equation in the standard form of a parabola with a vertex of (4,2) that passes through (2, 14)?

9514 1404 393

  y = 3x^2 -24x +50

Step-by-step explanation:

The vertex form is ...

  y = a(x -4)^2 +2

where 'a' is chosen to make the curve pass through the given point.

  14 = a(2 -4)^2 +2 . . . . substitute the given point

  14 = 4a +2 . . . simplify

  12 = 4a . . . . . subtract 2

  3 = a . . . . . . . divide by 4

Then the standard form is the expansion of the vertex form:

  y = 3(x -4)^2 +2 = 3(x^2 -8x +16) +2

  y = 3x^2 -24x +50