How do you find the equation for the power function y=kx^a with points (3,15) and (8,2). Also how do you find the quadratic equation in standard form containing points (3,26.6), (8,36.6), and (14, 13.4)? Help would be appreciated thank you!

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- Nov 17th 2006, 03:44 PMjarnyQuadratic/Power Function Help
How do you find the equation for the power function y=kx^a with points (3,15) and (8,2). Also how do you find the quadratic equation in standard form containing points (3,26.6), (8,36.6), and (14, 13.4)? Help would be appreciated thank you!

- Nov 17th 2006, 04:20 PMtopsquark
- Nov 17th 2006, 07:14 PMjarnyStill having a little trouble.....
Im still having a little trouble understanding the power function. The quadratic i get but could someone post the solution/way to do it so i can check my work? thanks

- Nov 17th 2006, 08:30 PMearboth
Hello, Jarny,

I take over topsquark's system of equation:

Quote:

is a system of two equations in two unknowns. So solve for a and log(k).

Plug in into the 2nd equation:

Rearrange with the variable**a**on one side of the equation:

You can rewrite the last equation to:

EB - Nov 18th 2006, 03:16 AMSoroban
Hello, jarny!

I assume you could use a walk-through ... with baby-steps.

. . Okay, here we go . . .

Quote:

Find the equation for the power function with points and

Divide**(1)**by**(2)**: .

Take logs: .

Hence: .

Substitute into**(1)**: .

Therefore, the power function is: .

. . . . . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Check

.*close enough!*

Quote:

Find the quadratic equation containing points

The quadratic function is of the form: .

.

Multiply**(4)**by

. . . . . . . Add**(5)**: .

And we have: .

Substitute into**(4)**: .

Substitute into**(1)**: .

Therefore: . . or .