An equation for a parabola that has a vertex at (4,2)

Question

And then simplified into standard form

Answer 1

Vertex Form of a parabola:

y = a ( x - h)² + k

where vertex is: (h, k)

In this exercise, vertex is (4, 2), and assuming that a = 1:

h = 4

k = 2

a = 1

The equation of the parabola in Vertex Form is:

y = 1 (x - 4)² + 2

Standard Form:

y = (x - 4)² + 2

y = ( x² - 2 • x • 4 + 4²) + 2

y = (x² - 8x + 16) + 2

y = x² - 8x + 16 + 2

y = x² - 8x + 18

Answer 2

y= (x-h)^2 + k

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

x=(y-k)^2 + h

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

replace (h,k) with (4,2) and you get a standard up or down, left or right, opening parabola with vertex (4,2)