1. parabola HW help plz

A, write an equation whose graph is a parabola whose vertex is (3/4,-3)

B, write an equation whose graph is a parabola that opens downward and has an axis of symmetry x=-4

C, Write an equation whose graph is a parabola opens upward and has a y-intercept of -1/2

D, Write an equation whose graph is a parabola whose vertex is (-3,4) with a y intercept of 1

2. OK here is what you do

A. the equation for a parabola with vertex $\displaystyle (h,k)$...is $\displaystyle y=a(x-h)^2+k$...so for $\displaystyle \frac{3}{4},-3)$...is $\displaystyle y=\bigg(x-\frac{3}{4}\bigg)^2-3$

B.the equation for a line facing down with its axis of symmetry at 4 is $\displaystyle y=-a(x+4)^2+k$

C.one of the possibilities $\displaystyle y=x^2-\frac{1}{2}$

D.to do this you need to set up your equation [tex]y=a(x+3)^2+4...I know...now all you have to do is say is put in your values $\displaystyle 1=a(0+3)^2+4$ and solve for a...so you get $\displaystyle a=\frac{-1}{3}$...so your equation is $\displaystyle y=\frac{-(x+3)^2}{3}+4$