Q: Sketch graphs of these three quadratics relations on the same set of axes
a) y=-3x2
b) y=1/4 x2
A: There are many ways to sketch graphs (quadratics). The most basic way is to: (1) make a table of values, (2) plot the points, (3) connect the dots.
So, let’s start with the first equation (a) y=-3x2 and make a table of values:
STEP 1
Start by picking values for x. I will pick -2, -1, 0, 1, 2 for x:
x | -2 | -1 | 0 | 1 | 2
y | | | | |
Now we need to calculate the y values.
When x = -2, y=-3(-2)2 = -3(4) = -12
When x = -1, y=-3(-1)2 = -3(1) = -3
When x = 0, y=-3(0)2 = -3(0) = 0
When x = 1, y=-3(1)2 = -3(1) = -3
When x = 2, y=-3(2)2 = -3(4) = -12
So, the table is complete:
x | -2 | -1 | 0 | 1 | 2
y | -12 | -3 | 0 | -3 | -12
STEP 2:
Plot the points: (-2, -12) (-1, -3) (0, 0) (1, -3) (2, -12) on the axes
STEP 3
Connect the dots to make a parabola. You should have a picture like so:
Now we need to do the same thing for equation (b) y=1/4 x2
STEP 1
Start by picking values for x. I will pick -2, -1, 0, 1, 2 for x:
x | -2 | -1 | 0 | 1 | 2
y | | | | |
Now we need to calculate the y values.
When x = -2, y=1/4 (-2)2 = 1/4 (4) = 1
When x = -1, y=1/4 (-1)2 = 1/4 (1) = 1/4
When x = 0, y=1/4 (0)2 = 1/4 (0) = 0
When x = 1, y=1/4 (1)2 = 1/4 (1) = 1/4
When x = 2, y=1/4 (2)2 = 1/4 (4) = 1
So, the table is complete:
x | -2 | -1 | 0 | 1 | 2
y | 1 | 1/4 | 0 | 1/4 | 1
STEP 2:
Plot the points: (-2, 1) (-1, 1/4) (0, 0) (1, 1/4) (2, 1) on the axes
STEP 3
Connect the dots to make a parabola. You should have a picture like so:
SO…. If we wanted to put these two graphs on the same axes, it would look something like (depending on your scale on the y-axis):
