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**+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

#1**+5 **

Best Answer

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