SOLUTION: find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4).

Question 1187647: find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4).

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The given information is unusual, so initially we don't have a good idea of where to go with the problem. So we do the only thing we can -- write the general form of the equation and use each the two given points in that equation to see what it gives us.

The vertex is on the line y=2x, so we can call the coordinates of the vertex (a,2a). Then the vertex form of the equation of a parabola parallel to the x-axis with vertex (a,2a) is

Plug in (x,y)=(1.5,1) and (x,y)=(3,4) to get two equations in a and p:

[1]

[2]

Subtract [1] from [2]:

[3]

Substitute [3] in [2]:

or

There will be two parabolas that satisfy the given conditions.

(1) a=3.5; 4p=10-8a=-18; 2a=7

(2) a=1; 4p=10-8a=2; 2a=2

Here is a graph of the two parabolas, one with vertex (1,2) and the other with vertex (3.5,7) and both passing through the points (1.5,1) and (3,4)

RELATED QUESTIONS
find the equation of a parabola with vertex on the line y=2x, axis parallel to the y axis (answered by ikleyn)

Find the equation of a parabola with vertex on the line y = x + 2, axis parallel to Oy,... (answered by MathLover1)

What is the equation of a parabola with vertex on the line y=x, axis parallel to Ox, and... (answered by KMST,advanced_Learner)

find the equation of the parabola With the vertex on the y axis, axis of symmetry... (answered by stanbon)

find the equation of the parabola with vertex on the line y=x, the axis of parabola is... (answered by josgarithmetic,lwsshak3)

Find the equation of a parabola with axis parallel to the x-axis and passing through... (answered by Boreal)

Find the equation of the parabola with vertex on the line y = 2, axis parallel to Oy,... (answered by greenestamps)