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What is the equation of the parabola that has a vertex at # (3, 3) # and passes through point # (13, 6) #?

Answer 1

Julia Adams

The equation is #y=3/100(x-3)^2+3#

The equation of the parabola is

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

Where #(h,k)# is the vertex

Therefore,

#h=3# and #k=3#

So, the equation is

#y=a(x-3)^2+3#

The parabola pases through the point #(13,6)#

so,

#6=a(13-3)^2+3#

#100a=3#

#a=3/100#

The equation is

#y=3/100(x-3)^2+3#

graph{y=3/100(x-3)^2+3 [-36.52, 36.54, -18.27, 18.28]}

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Answer 2

Savannah Anderson

To find the equation of the parabola with a vertex at (3, 3) and passing through point (13, 6), use the vertex form of a parabola equation:

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

where (h, k) is the vertex.

Substitute the vertex coordinates into the equation: y = a(x - 3)^2 + 3
Use the given point (13, 6) to find the value of 'a': 6 = a(13 - 3)^2 + 3
Solve for 'a': 6 = a(10)^2 + 3 6 = 100a + 3 100a = 3 a = 3/100
Substitute the value of 'a' back into the equation: y = (3/100)(x - 3)^2 + 3

Therefore, the equation of the parabola is: y = (3/100)(x - 3)^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.