Graph the quadratic equation after completing the given table of values. y = x^2 – 2x?
To graph the quadratic equation y = x^2 - 2x, you can complete a table of values and plot the points on a coordinate plane.
To start, choose a range of x-values and substitute them into the equation to find the corresponding y-values. Let's say we select x-values from -3 to 3.
When x = -3:
y = (-3)^2 - 2(-3) = 9 + 6 = 15
So, the first point is (-3, 15).
When x = -2:
y = (-2)^2 - 2(-2) = 4 + 4 = 8
The second point is (-2, 8).
When x = -1:
y = (-1)^2 - 2(-1) = 1 + 2 = 3
The third point is (-1, 3).
When x = 0:
y = (0)^2 - 2(0) = 0
The fourth point is (0, 0).
When x = 1:
y = (1)^2 - 2(1) = 1 - 2 = -1
The fifth point is (1, -1).
When x = 2:
y = (2)^2 - 2(2) = 4 - 4 = 0
The sixth point is (2, 0).
When x = 3:
y = (3)^2 - 2(3) = 9 - 6 = 3
The seventh point is (3, 3).
Now, plot these points on a coordinate plane. Connect the points smoothly, and you will have the graph of the quadratic equation y = x^2 - 2x.
Note: Since we have a quadratic equation, the graph will be a parabola.