SOLUTION: A quadratic function is given. f(x) = {{{ x^2 - 4x }}} (a) Express the quadratic function in standard form. f(x) = (b) Find its vertex and its x- and y-intercept(s). (

Algebra ->  Functions -> SOLUTION: A quadratic function is given. f(x) = {{{ x^2 - 4x }}} (a) Express the quadratic function in standard form. f(x) = (b) Find its vertex and its x- and y-intercept(s). (      Log On


   

Question 906170: A quadratic function is given.
f(x) = +x%5E2+-+4x+
(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(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-4x is not a square and what you want is a square. You have so far, something which can
be matched to a rectangle area, x%28x-4%29. If you ADD and SUBTRACT %28-4%2F2%29%5E2=4, you can complete the square
and part of the resulting expression can be factored:

f%28x%29=x%5E2-4x%2B4-4
f%28x%29=%28x%5E2-4x%2B4%29-4
highlight%28f%28x%29=%28x-2%29%5E2-4%29----standard form.

The vertex is (2,-4), and because coefficient on the squared expression is POSITIVE 1,
this vertex is a minimum.

If you want to know the x-intercepts, solve for x in highlight_green%28%28x-2%29%5E2-4=0%29, a very simple
and easy process.

Finding y-intercept just means let x=0 and evaluate y.