Question 64443This question is from textbook algebra II
: This looks very vexing to me because I dont' understand it. Help!
Graph f(x) 3x^2-6x-1. plot at least 5 points.
Of those 5 points, state the vertex point, whether the vertex point is maximum or minimum and the equation of axis of symmetry.
This question is from textbook algebra II
Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Graph: 
Here's the graph:
The equation of the line of symmetry is given by:
 The a and the b come from the general form of the quadratic equation: 
In your equation, a = 3 and b = -6, so:
 is the equation of the line of symmetry.
Since the line of symmetry passes thrugh the vertex, you can find the coordinates of the vertex by substituting x = 1 into the quadratic equation and solving for y.
 Substitute x=1 and solve for y.
 Simplify.
The vertex point is at (1, -4) Confirm this on the graph.
The graph shows that the vertex point is a minimum.
To find four more points to meet your requirement, simply choose four conveniently small values of x and substitute these, one-by-one into the quadratic equation and solve for four values of y.
Let x = 0 for point1.
Point1 is (0, -1)
Let x = 1 for point2. You've got this one already, it's the vertex point (1, -4)
Let x = 2 for point3.
Point3 is (2, -1)
I hesitate to deprive you of the pleasure of doing your own math so perhaps you can finish this yourself.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Graph f(x)= 3x^2-6x-1. plot at least 5 points.
Of those 5 points, state the vertex point, whether the vertex point is maximum or minimum and the equation of axis of symmetry.
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If x=0 y=-1
If x=1 y=3-6-1=-4
If x=-1 y=3+6-1=8
If x=2 y==12-12-1=-1
If x=-2 y=12+12-1=23
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Complete the square to find the vertex and axis of symmetry:
3x^2-6x=y+1
3(x^2-2x)=y+1
x^2-2x=(1/3)(y+1)
Complete the square:
x^2-2x+1=(1/3)(y+1)+1
(x-1)^2=(1/3)(y+1+3)
(x-1)^2=(1/3)(y+4)
So, Vertex = (1,-4) is a minimum point because the parabola opens up.
Axis of symmetry is x=1
Cheers,
Stan H.
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