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# The vertex of the parabola is on the line y = 20. The y intercept is 15, and 3 is a zero of

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The vertex of the parabola is on the line y = 20. The y intercept is 15, and 3 is a zero of

the equation of the parabola. There are two possible parabolas that fit this description.

Find the equations of the two parabolas described.
Guest Jan 4, 2015

#1
+26396
+5

The general equation for a parabola can be written as: (x - h)2 = 4a(y - k)  where (h, k) are the coordinates of the vertex.

Since we are told that y = 20 at the vertex, then we know immediately that k = 20.

The y-intercept occurs where x = 0, so we have:  (0 - h)2 = 4a(15 - 20)    ...(1)

A zero of the equation means the value of x where y = 0, so we also have:  (3 - h)2 = 4a(0 - 20)    ...(2)

Can you use equations (1) and (2) to find two sets of values for h and a?

.

Alan  Jan 5, 2015
Sort:

#1
+26396
+5

The general equation for a parabola can be written as: (x - h)2 = 4a(y - k)  where (h, k) are the coordinates of the vertex.

Since we are told that y = 20 at the vertex, then we know immediately that k = 20.

The y-intercept occurs where x = 0, so we have:  (0 - h)2 = 4a(15 - 20)    ...(1)

A zero of the equation means the value of x where y = 0, so we also have:  (3 - h)2 = 4a(0 - 20)    ...(2)

Can you use equations (1) and (2) to find two sets of values for h and a?

.

Alan  Jan 5, 2015

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