SOLUTION: Write the vertex form equation of the parabola with vertex (10,0), axis of symmetry: y = 0, length of latus rectum = 1, a < 0

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Question 1041715: Write the vertex form equation of the parabola with vertex (10,0), axis of symmetry: y = 0, length of latus rectum = 1, a < 0
Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex form equation of the parabola with vertex (h,k), 
axis of symmetry: y = k, length of latus rectum = |4a|
is:

(y-k)² = 4a(x-h)

Substitute h=10, k=0, a=-1/4 since |4a|=1 and a < 0.

Edwin

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Concave to the left, and axis of symmetry is the x-axis. Some equation of parabola x=a%28y-0%29%5E2-10 or as x=ay%5E2-10. You do not know the value of a but you only know a%3C0.

Latus Rectum of 1 and the sign of a means that the focus is to the LEFT of the vertex. Both focus AND vertex are on the axis of symmetry, so x=0, and y=1/2 for the point (0, 1/2) as a endpoint for the latus rectum. Other endpoint is (0, -1/2 ).

Using either endpoint for the latus recturm, 0=a%281%2F2%29%5E2-10 with the values substituted, and you can calculate and pick the correct value for "a".