Question

Write the vertex form for a parabola with the given characteristics.
vertex ( 0, 0) directrix x = -15
Help Please!

Answer 1

well the distance from the vertex to the directrix is the focal length so a = 15

even though the drectrix is x = -15 the distance from the vertex is 15 units.

ans since the directrix is below the vertex the parabola is concave up.

the parabola will be in the form

\[(x -h)^2 = 4a(y -k)\]

(h, k) is the vertex and a is the focal length.

in your question you know h = 0 and k = 0

so just substitute h, k and a to find the parabola

Answer 2

so I'm looking for Y

Answer 3

nope.. h = 0 and k = 0

gives

\[(x -0)^2 = 4a(y - 0)... or ... x^2 = 4ay\]

now substitute a = 15 into the equation

\[x^2 = 4 \times 15 \times y\]

just simplify it