How do you write standard form of equation of the parabola that vertex is (2,3) and graph passes through the given point (0,2)?

1 Answer
Mar 19, 2018

Answer:

The equation of parabola is #y = -1/4(x-2)^2+3 #.

Explanation:

The vertex form of equation of parabola is

#y = a(x-h)^2+k ; (h,k)# being vertex , here #h=2 , k=3 #

So the equation of parabola is #y = a(x-2)^2+3 ;#. The parabola

passes through point #(0,2) :.# the point will satisfy the equation

of parabola. Putting #x=0 and y=2# in the equation we get,

#2=a(0-2)^2+3 or 2= 4a+3 or 4a= 2-3 #or

# 4a=-1 or a= -1/4#. Hence ,the equation of parabola is

#y = -1/4(x-2)^2+3 #.

graph{-1/4(x-2)^2+3 [-10, 10, -5, 5]} [Ans]