# What is the equation of the parabola that has a vertex at # (77, 7) # and passes through point # (82,32) #?

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The equation of the parabola with a vertex at (77, 7) and passing through point (82, 32) is:

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

Where (h, k) is the vertex.

Substitute the vertex coordinates:

y = a(x - 77)^2 + 7

To find the value of 'a', use the point (82, 32):

32 = a(82 - 77)^2 + 7

Solve for 'a':

32 = a(5)^2 + 7 32 = 25a + 7 25a = 32 - 7 25a = 25 a = 1

So, the equation of the parabola is:

y = (x - 77)^2 + 7

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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.

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.

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.

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