What is the equation of the parabola that has a vertex at # (-1, 6) # and passes through point # (3,22) #?

1 Answer
Binayaka C.
Jan 22, 2016

Equation of the parabola is # y= x^2+2*x+7#

Explanation:

We use here the standard equation of Parabola #y= a (x-h)^2 +k# Where h an k are the co-ordinates of Vertex. Here h = -1 and k=6 (given) So the equation of the Parabola becomes # y = a(x+1)^2+6#. Now the Parabola passes through the point (3,22). So this point will satisfy the Equation. Then #22 = a(3+1)^2+6# or #a*16=22-6 or a=1#
So the Equation of the parabola is # y= 1*(x+1)^2+6 or y= x^2+2*x+7#[Answer] graph{x^2+2x+7 [-80, 80, -40, 40]}

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