What is the equation of the parabola that has a vertex at # (2, -1) # and passes through point # (3,-4) #?

1 Answer
Mr. Mike
Apr 17, 2018

#y=-3x^2+12x-13#

Explanation:

This problem will be easier if we express the equation for the parabola in vertex form.

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

where #k# is the #x#-coordinate of the vertex and #h# is the #y#-coordinate of the vertex. Since the vertex is at #(2, -1)# our equation for the parabola becomes

#y=a(x-2)^2-1#

Since the parabola passes through the point #(3, -4)# we can write

#-4=a(3-2)^2-1=a-1#

and solve for #a# by adding 1 to both sides.

#a=-3#

So the equation for the parabola is

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

We can expand the binomial to obtain the equation for the parabola in standard form.

#y=-3(x^2-4x+4)-1=-3x^2+12x-13#

graph{-3x^2+12x-13 [-1, 4, -10, 5]}

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