SOLUTION: A quadratic function is given. f(x) = −x^2 + 10x (a) Express the quadratic function in standard form. f(x) = ____ (b) Find its vertex and its x- and y-intercept(s). (I

Algebra ->  Functions -> SOLUTION: A quadratic function is given. f(x) = −x^2 + 10x (a) Express the quadratic function in standard form. f(x) = ____ (b) Find its vertex and its x- and y-intercept(s). (I      Log On


   

Question 906407: A quadratic function is given.
f(x) = −x^2 + 10x
(a) Express the quadratic function in standard form.
f(x) = ____
(b) Find its vertex and its x- and y-intercept(s). (If an answer does not exist, enter DNE.)
vertex...............(x, y) = ( _ , _ )
x-intercepts (x, y) = ( _ , _ ) (smaller x-value)
........................(x, y) = ( _ , _ ) (larger x-value)
y-intercept (x, y) = ( _ , _ )


Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-x%5E2%2B10x
f%28x%29=-1%28x%5E2-10x%29
The term to complete the square is %28-10%2F2%29%5E2=25
Add AND subtract 25 INSIDE the parenthesized part of the definition for f.

That is just to get started for putting f(x) into standard form (vertex form).
You do the rest.

Check this lesson and study it to understand how all of this works:
http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev