SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.
f(x)=3x^2-12x+3
1. What is the vertex
2. What is the
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Question 626175: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.
f(x)=3x^2-12x+3
1. What is the vertex
2. What is the equation of the line of symmetry
3. What is the maximum/minimum of F(x)
4. Is the value, f(x)= -9 a minimum or a maximum?
Please graph. Thank you very much up front.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The vertex of the parabola defined by \ =\ ax^2\ +\ bx\ +\ c)
is the point )
where 
and )
.
The equation of the axis of symmetry is 
The maximum or minimum of )
is 
. If the lead coefficient is positive, i.e. 
, then the parabola opens upward and the vertex is a minimum. If the lead coefficient is negative, i.e. 
, the parabola opens downward and the vertex is a maximum.
Graph: Plot the vertex. Plot the point )
which is the 
-intercept. Then by symmetry, )
is also on the graph. Set the function equal to zero and solve for the two roots 
and 
(use the quadratic formula or complete the square since your example doesn't factor). Plot the two points, )
and )
. That gives you 5 points through which you can draw a smooth curve.
If you want more points, pick a convenient distance 
from the vertex. Then calculate the value of the function )
, then plot the point \right))
. Then, by symmetry you can also plot \right))
. You can repeat this process with as many different values of as you like.
John
My calculator said it, I believe it, that settles it
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