SOLUTION: Find the vertex of the following quadratic function, and find any intercepts. Also determine the graph of the function. f(x)= x^2-6x+10

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the vertex of the following quadratic function, and find any intercepts. Also determine the graph of the function. f(x)= x^2-6x+10      Log On


   

Question 603088: Find the vertex of the following quadratic function, and find any intercepts. Also determine the graph of the function.
f(x)= x^2-6x+10
Found 2 solutions by lwsshak3, stanbon:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex of the following quadratic function, and find any intercepts. Also determine the graph of the function.
f(x)= x^2-6x+10
**
complete the square
y=(x^2-6x+9)+10-9
y=(x-3)^2+1
vertex: (3,1)
..
x-intercepts
set y=0
(x-3)^2+1=0
(x-3)^2=-1
x-intercepts: none
..
See graph below:
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E2-6x%2B10%29+



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex of the following quadratic function, and find any intercepts. Also determine the graph of the function.
f(x)= x^2-6x+10
-----
Complete the square:
f(x) = x^2-6x+9 + 10-9
---
f(x) = (x-3)^2 + 1
---
Vertex: (3,1)
---
x-intercepts(s)
Solve (x-3)^2 + 1 = 0
None
----
y-intercepts
Let x = 0; then y = 10
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Cheers,
Stan H.
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