Question

what is the equation of the parabola that opens to the left, has its vertex at the origin and passes through (-2,3)???

Answer 1

not even close...

Answer 2

If a parabola opens sideways, which variable is squared, x or y?

Answer 3

y is squared

Answer 4

How do you know?

Answer 5

The squaring of the variables in the equation of the parabola determines where it opens: When y is squared and x is not, the axis of symmetry is horizontal and the parabola opens left or right.

Answer 6

Right. Now, the vertex is at the origin, so we don't even have to subtract anything from either variable to translate it. So, our equation will look like\[y^{2} = cx\]How might we find c?

Answer 7

this is where im lost

Answer 8

What was the other piece of information they gave us in the problem?

Answer 9

vertex passes through the origin

Answer 10

I used that when I said we didn't have to subtract from x or y to translate the parabola.

What have we not yet used?

Answer 11

the points (-2,3)

Answer 12

Right. How can we use that fact and y^2 = cx to find c?

Answer 13

y^2=c(-2)

Answer 14

Close. We know the point (-2, 3) will lie on the graph of our equation. That means (-2, 3) has to be a solution to our equation, y^2 = cx.

Answer 15

so y^2 =3^2=9 2/9y?

Answer 16

no, -(9/2)y

Answer 17

x...

Answer 18

Remember, the point (-2, 3) means x=-2 and y=3. We can plug both of those numbers in to our equation.
y^2 = cx
3^2 = c(-2)
c = -(9/2)
So putting it all together, what will the final equation be?

Answer 19

y^2=-(9/2)x

Answer 20

Excellent!

Answer 21

thanks for the help!