Write an equation of the parabola that passes through the points at (-3,7), has its vertex at (-1,3), and opens to the left?

Question

anonymous · Answer

Start with the equation $y = ax^2$ of a general parabola that opens upward and has its vertex at the origin.

anonymous · Answer

Sorry, opens vertically. It might open downward.

anonymous · Answer

We want it to open to the left so we interchange $x$ and $y$: $x = ay^2$.

anonymous · Answer

We want its vertex to be $(-1, 3)$ so we translate it by replacing $x$ with $x+1$ and $y$ with $y-3$: $x+1=a(y-3)^2$.

anonymous · Answer

We know that (-3, 7) satisfies the equation of our parabola: $$(-3)+1=a((7)-3)^2\-2 = 16a\a = -1/8$$
In conclusion, the equation is $$x+1=-(y-3)^2/8$$

anonymous · Answer

Thank you! I

anonymous · Answer

You're welcome!