How do I graph this function y = x(4 - 2x)(6 - 2x) I am not
sure where you receive the points from.
Thanks, Christine
First find the three x-intercepts by substituting 0 for y
y = x(4 - 2x)(6 - 2x)
0 = x(4 - 2x)(6 - 2x)
Use the zero-factor principle, that is set each factor
equal to 0 and solve for x
The factors are x, (4 - 2x) and (6 - 2x)
Setting x = 0, just gives x = 0
Setting 4 - 2x = 0 gives x = 2
Setting 6 - 2x = 0 gives x = 3
So the three x-intercepts are (0, 0), (2, 0), and (3, 0)
Plot those. Now we choose a value of x just less than x = 0,
say x = -1, and substitute it for x in
y = x(4 - 2x)(6 - 2x)
y = -1(4 - 2(-1))(6 - 2(-1))
y = -1(4 + 2)(6 + 2)
y = -1(6)(8)
y = -48
So plot the point (-1, -48)
Now we choose a value of x between x = 0 and x = 2,
say x = 1, and substitute it for x in
y = x(4 - 2x)(6 - 2x)
y = 1(4 - 2(1))(6 - 2(1))
y = 1(4 - 2)(6 - 2)
y = 1(2)(4)
y = 8
So plot the point (1, 8)
Now we choose a value of x between x = 2 and x = 3,
say x = 2.5, and substitute it for x in
y = x(4 - 2x)(6 - 2x)
y = 2.5(4 - 2(2.5))(6 - 2(2.5))
y = 2.5(4 - 5)(6 - 5)
y = 2.5(-1)(1)
y = -2.5
So plot the point (2.5, -2.5)
Finally we choose a value of x just more than x = 3,
say x = 4, and substitute it for x in
y = x(4 - 2x)(6 - 2x)
y = 4(4 - 2(4))(6 - 2(4))
y = 4(4 - 8)(6 - 8)
y = 4(-4)(-2)
y = 32
So plot the point (4, 32)
Now draw a smooth curve through those points moving from left to right:
Connect (-1,-48) to (0,0)
Connect (0,0) to (1,8)
Connect (1,8) to (2,0)
Connect (2,0) to (2.5,-2.5)
Connect (2.5,-2.5) to (3,0)
Connect (4,0) to (4,32)
Edwin McCravy
AnlytcPhil@aol.com