Formulas for Quadratic Functions

find a formula for the quadratic function whose graph has these properties:

a. A vertex at (3,1) and a y intercept of y = 9

y = a (x-h) ^ 2

vertex (3,1) : h = 3, k = 1
y intercept of y = 9

y = a(x - 3) ^ 2 + 1
9 = a (0 - 3) ^ 2 + 1
9 = 9a + 1

minus 1 on both sides

8 = 9a

divide 9 by both sides

a = 8/9

y = 8/9 (x - 3) ^ 2 + 1

to have the formula in standard form :

(x-3)(x-3) = x^2 - 6x + 9

y = 8/9 (x^2 - 6x + 9) + 1
y = 8/9 x^2 - 16/3x + 8 + 1
y = 8/9x^2 - 16/3x + 9


is this correct?

looks fine.

you can check the x-value of the vertex ...

x = -b/(2a) = (16/3)/(16/9) = 9/3 = 3

sweetliljenny said:

y = a (x-h) ^ 2

Click to expand...

The formula for a parabola with vertex at (h, k) is as follows:

. . . . .y = a(x - h)² + k

I'm not sure how you ended up with "a = 8/9" without having "k" in your formula, but that is the correct value.

For clarity's sake (if you're required to give your answer in multiplied-out form), use grouping symbols:

. . . . .y = (8/9)x² - (16/3)x + 9

I get the same equation. Good job!

Eliz.