SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic fuction, and graph the function. {{{f(x)=3x^2-12x+16}}} The vertex is ___ (Type an ordere

Algebra ->  Graphs -> SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic fuction, and graph the function. {{{f(x)=3x^2-12x+16}}} The vertex is ___ (Type an ordere      Log On


   



Question 394799: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic fuction, and graph the function.
f%28x%29=3x%5E2-12x%2B16
The vertex is ___ (Type an ordered pair.)
The line of symmetry is:
A. y=4
B. x=2
C. x=-2
D. y=-4
The maximum/minimum of f(x) is ___.
Is the value, f(2)=4 a minimum or a maximum?
Graph.

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic fuction, and graph the function.
f(x)=3x^2-12x+16
---
Vertex occurs at x = -b/(2a) = 12/(6) = 2
f(2) = 3*2^2-12*2+16 = 12-24+16 = 4
The vertex is (2,4) (Type an ordered pair.)
The line of symmetry is x=2
-----------
A. y=4
B. x=2
C. x=-2
D. y=-4
The maximum/minimum of f(x) is (2,4).
Is the value, f(2)=4 a minimum or a maximum?
Minimum
-----------------
Graph.
graph%28400%2C300%2C-10%2C10%2C-10%2C20%2C3x%5E2-12x%2B16%29
================
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Given



The -coordinate of the vertex is given by:



The -coordinate of the vertex is given by:



Hence the vertex is:



The line of symmetry is:



The maximum or minimum value is

If then the parabola opens upward and is a minimum. If then the parabola opens upward and is a maximum.



John

My calculator said it, I believe it, that settles it
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