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!
Hello, Jarny,
I take over topsquark's system of equation:
From the first equation you get:
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
Hello, jarny!
I assume you could use a walk-through ... with baby-steps.
. . Okay, here we go . . .
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!
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 .