# Thread: Introuduction to Conics problems

1. ## Introuduction to Conics problems

I cannot understand these for the life of me.

"Find the standard form of the equation of the parabola with its vertex at the origin"

1. Focus (2,0)
2. Focus: (0,-2)
3. Directrix: Y=3
4. Directrix: Y=-3

"Find the Standard form of the equation of the parabola"
1. Vertex (-1,2) Focus (-1,0)

2. Originally Posted by bstewart09
I cannot understand these for the life of me.

"Find the Standard form of the equation of the parabola"
1. Vertex (-1,2) Focus (-1,0)
Hi bstewart09,

Vertex (-1, 2) means (h, k). h = -1, and k = 2 in the equation $\displaystyle y=a(x-h)^2+k$.

Focus (-1, 0) means $\displaystyle \left(h, k+\frac{1}{4a}\right)$. The parabola opens downward and $\displaystyle k+\frac{1}{4a}=0$.

$\displaystyle 2+\frac{1}{4a}=0$

Solving the above equation for a yields $\displaystyle a=-\frac{1}{8}$

Substituting back into the vertex form of the equation, we get:

$\displaystyle y=-\frac{1}{8}(x+1)^2+2$

You can convert this equation into $\displaystyle y=ax^2+bx+c$