SOLUTION: Given the function y=4x-x^2 1.determine of the vertex function. 2.determine the intercepts of the function.

Algebra ->  Rational-functions -> SOLUTION: Given the function y=4x-x^2 1.determine of the vertex function. 2.determine the intercepts of the function.      Log On


   

Question 1073022: Given the function y=4x-x^2
1.determine of the vertex function.
2.determine the intercepts of the function.
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to get the function into vertex form,
y=-x%5E2%2B4x
y=-%28x%5E2-4x%29
y=-%28x%5E2-4x%2B4%29%2B4
y=-%28x-2%29%5E2%2B4
So the vertex is,
(2,4)
So then using the vertex form,
-%28x-2%29%5E2%2B4=0
%28x-2%29%5E2=4
x-2=0+%2B-+2
x=2+%2B-+2
x=4 and x=0
.
..
...
.

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
For the vertex, the problem was solved in 

https://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.1073021.html


https://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.1073021.html


The intercepts are (0,0) and (4,0).


The x-intercepts are the roots of this quadratic equation

-x^2 + 4x = 0,


which is factored as x*(4-x) = 0  and immediately gives you the roots x =  and x = 4.


The y-intercept is the value of the function -x%5E2%2B4x at x = 0.
This value is 0.