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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