The parabola has the turning point at (z, -8) and y-intercept at 10, and an x-intercept at x=5.

What is --- value of z?

The equation of parabola?

Plz help!

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- Mar 24th 2008, 03:16 AMmibamarsParabola Question! Help!
The parabola has the turning point at (z, -8) and y-intercept at 10, and an x-intercept at x=5.

What is --- value of z?

The equation of parabola?

Plz help! - Mar 24th 2008, 03:48 AMmr fantastic
There are several approaches that can be taken. This is one of them:

The equation can be written in turning point form as .

Substitute the known points (0, 10) and (5, 0) to get two equations in the unknowns a and z. Solve these two equations simultaneously to get the values of a and z. - Mar 24th 2008, 04:04 AMmibamars
Still cant solve it. Stuck on the unknown values. Can someone do a full solve?

- Mar 24th 2008, 04:14 AMtopsquark
- Mar 24th 2008, 05:23 AMmr fantastic
- Mar 24th 2008, 05:31 AMSoroban
Hello, mibamars!

Another approach . . .

Quote:

The parabola has the turning point at ,

and y-intercept at , and an x-intercept at

Find and the equation of the parabola.

The general equation of a parabola is: .

We are given three points on the parabola.

We are told that: .

We have: .

And we have: .

Substitute into [3]: .

Substitute [4] and [5] into [1]: .

. . and we have: .

There are__two__solutions . . .

. .

- Mar 24th 2008, 01:40 PMtopsquark