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What is the equation of the parabola that has a vertex at # (-11, 3) # and passes through point # (13,5) #?

Answer 1

#576y = 2(x+11)^2 + 1728#

The vertex form of a parabola is #y = a(x-b)^2 +c# where the vertex is #(b,c)# Therefore #y = a(x+11)^2 +3# By using the coordinates of the given point we can find a #5 = a(13 + 11)^2 +3# #a = (5-3)/24^2 = 2/576#

#576y = 2(x+11)^2 + 1728#

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Answer 2

Isaiah Anthony

The equation of the parabola in vertex form is:

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

where (h, k) is the vertex.

Given the vertex (-11, 3), we have h = -11 and k = 3.

Substituting these values into the equation:

y = a(x + 11)^2 + 3

To find the value of 'a', we use the point (13, 5) which lies on the parabola.

Substituting x = 13 and y = 5 into the equation:

5 = a(13 + 11)^2 + 3

Solving for 'a':

5 = a(24)^2 + 3 5 = a(576) + 3 2 = 576a a = 2/576 a = 1/288

Substitute 'a' back into the equation:

y = (1/288)(x + 11)^2 + 3

Therefore, the equation of the parabola is:

y = (1/288)(x + 11)^2 + 3.

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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.