SOLUTION: Hello, how do i fint the vertex and intercepts for this quadratic function: f(x) = x^2 - 6x thank you!

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Question 65159This question is from textbook algebra for college students
: Hello,
how do i fint the vertex and intercepts for this quadratic function:
f(x) = x^2 - 6x

thank you! This question is from textbook algebra for college students

Found 3 solutions by josmiceli, funmath, cristiana:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+-+6x
f%28x%29+=+x%28x+-+6%29
The intercepts are (0 , 0) and (6 , 0)
The axis of symmetry will be midway between x = 0 and x = 6
which would be x = 3
f%28x%29+=+3%5E2+-+6%2A3
f%28x%29+=+9+-+18
f%28x%29+=+-9
So the vertex is at (3 , -9)

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^2 - 6x
There are a couple of ways to find the vertex, if your teacher is putting the equation in vertex form, let me know and I'll redo this.
When a quadratic equation is in this form: f(x)=ax^2+bx+c, I prefer using this formula to find the x coordinate of the vertex: highlight%28x=-b%2F2a%29
a=1, b=-6 and c=0
x=-%28-6%29%2F%282%281%29%29
x=6%2F2
x=3
To find the y-coordinate find f(3)
f%283%29=%283%29%5E2-6%283%29
f%283%29=9-18
f%283%29=-9
The vertex (x,y)=(3,-9)
You find the y-intercept, by letting x=0:
f%280%29=%280%29%5E2-6%280%29
f%280%29=0-0
f%280%29=0
The y-intercept is (0,0) The origin will be both an x and a y-intercept.
To find the x-intercept, let f(x)=0 and solve for x.
0=x%5E2-6x
0=x%28x-6%29
x=0 and x-6=0
x=0 and x=6
The x-intercepts are (0,0) and (6,0)
Here's what it looks like:
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-6x%29
Happy Calculating!!!

Answer by cristiana(10) About Me  (Show Source):
You can put this solution on YOUR website!
To easily determine the vertex we have to bring the function to the following form:
y+=+a%28x-h%29%5E2%2Bk and the vertex is: (h,k)
To do that, we basically need to complete the square
x%5E2-6x+=+x%5E2+-+2%2A3x+%2B+9+-+9+=+%28x-3%29%5E2+-9
Therefore, our new form is:
y+=+%28x-2%29%5E2+-9
We can now spot the vertex: (2,9)

To determine the intercepts, we simply have to solve the equation:
x%5E2-6x+=0
Solutions: {0, 6} - these are the x-intercepts

Hope it helped,
Cristiana