Write the equation of a parabola with vertex (2,-1) and directrix y=-3

Question

asked Jul 7, 2021 89.9k views

1 Answer

Cojones · Answer 1 · 2021-07-12T01:37:35+0000

Answer:

y=-x^(2) -3x-3

Explanation:

a parabola is the graph of a quadratic equation, so the general equation is

y=ax^(2) +bx+c

If the directrix is negative, it means the graph opens down, so a is -

and c is -3

this gives us

y=-x^(2) +bx-3

all we need now is what is b

b is the y intercept for
y=mx+b

to find the y intercept, we plug in 0 for x

$y=-x^(2) +bx-3\\y=-0^(2) +b(0)-3\\y=0+0-3\\y=-3$

so the y intercept is -3

so the equation is

y=-x^(2) -3x-3