SOLUTION: PROBLEM:
GIVEN THE FUNCTION DEFINED BY: f(x)=x^2-6x+12
A) IDENTIFY THE VERTEX OF THE PARABOLA.
B)DOES THIS PARABOLA OPEN UP OR DOWN?
C)DOES THE VERTEX REPRESENT THE MAXIMUM OR
Algebra.Com
Question 138847: PROBLEM:
GIVEN THE FUNCTION DEFINED BY: f(x)=x^2-6x+12
A) IDENTIFY THE VERTEX OF THE PARABOLA.
B)DOES THIS PARABOLA OPEN UP OR DOWN?
C)DOES THE VERTEX REPRESENT THE MAXIMUM OR MINIMUM POINT OF THE FUNCTION?
D)WHAT IS THE MAXIMUM OF MINIMUM VALUE OF THE FUNCTION f?
E) WHAT IS THE AXIS OF SYMMETRY FOR THIS PARABOLA?
*** IN THIS PROBLEM I HAVE NO UNDERSTANDING OF ANY OF THIS.. I TRIED LOOKING IN THE BOOK FOR A SOLUTION,BUT STILL NO LUCK.. PLEASE HELP???!!
THANKS, lj23kfuller@yahoo.com
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
GIVEN THE FUNCTION DEFINED BY: f(x)=x^2-6x+12
A) IDENTIFY THE VERTEX OF THE PARABOLA.
You have a quadratic with a=1 , b=-6, and c = 12
The vertex occurs where x = -b/2a = 6/2 = 3
The corresponding y-value is f(3) = 9-18+12 = 3
The vertex is (3,3)
-----------------------------
B)DOES THIS PARABOLA OPEN UP OR DOWN?
Since the coefficient of the x^2 term is positive, the parabola
opens upward.
----------------------------
C)DOES THE VERTEX REPRESENT THE MAXIMUM OR MINIMUM POINT OF THE FUNCTION?
Because of what is said in part B, the vertex is a minimum point.
----------------------------
D)WHAT IS THE MAXIMUM OF MINIMUM VALUE OF THE FUNCTION f?
There is no maximum f value; the minimum value is 3 which occurs where x=3.
------------------------------
E) WHAT IS THE AXIS OF SYMMETRY FOR THIS PARABOLA?
The axis of symmetry is the vertical line thru the vertex, or x = 3.
==================================================
==================================================
Cheers,
Stan H.
RELATED QUESTIONS
f(x) = 2(x-3)2 + 1 find the coordinates of the vertex parabola defined by the given... (answered by Fombitz)
in the following exercise, find the coordinates of the vertex for the parabola defined by (answered by shree840)
f(x) = -3 (x-2)2 + 12 find the coordinates of the vertex for the parabola defined by... (answered by Fombitz)
The problem I need help with is: Find the coordinates of the vertex for the parabola... (answered by ewatrrr)
f(x) = -2x2 + 8x -1 find the cooordinates of the vertex for the parabola defined by the (answered by Fombitz)
Find the coordinates of the vertex for the parabola defined by the given quadratic... (answered by Boreal)
In the following exercise, find the coordinate of the vertex for the parabola defined by... (answered by richwmiller)
find the coordinates of the vertex for the parabola defined by the given quadratic... (answered by robertb)
Find the x-coordinate of the vertex of the parabola defined by the function
f(x)=... (answered by josgarithmetic,MathTherapy)