Question

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

Answer 1

`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`