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What is the equation of the parabola that has a vertex at # (-1, 16) # and passes through point # (3,32) #?

Answer 1

Eva Abramson

#y-16 = (x+1)^2#

A parabola with vertex #(h,k)# has an equation of the form:

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

So this parabola is #y-16=a(x_1)^2#.

Using the fact that when #x=-1#, we have #y = 32# we can find #a#.

#32 - 16 = a(3+1)^2#

So #a = 1#

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Answer 2

Avery Alexander

The equation of the parabola that has a vertex at (-1, 16) and passes through point (3,32) is y = 2(x + 1)^2 + 16.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.