Question

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

Answer 1

Answer:

$y=-x^{2} -3x-3$

Step-by-step 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

$y=-x^{2} -3x-3$