graph y=-2x and y=-x squared
what points do the graphs have in common?
Describe how the graphs are different.
-x2=-2x
x=2, y=-4 are the common points.
To find the points where the two graphs intersect, you need to set the two equations equal to each other and solve for x-coordinate:
-2x = -x^2
Rearrange the equation:
x^2 - 2x = 0
Factor out x:
x(x - 2) = 0
So, we have two possibilities for x:
1) x = 0
2) x - 2 = 0 ⇒ x = 2
Now, substitute these values back into one of the equations (for example, y = -2x) to find the corresponding y-coordinates:
1) When x = 0, y = -2(0) = 0, so one point of intersection is (0, 0).
2) When x = 2, y = -2(2) = -4, so the other point of intersection is (2, -4).
Therefore, the graphs intersect at the points (0, 0) and (2, -4).
Now, let's compare the graphs:
The equation y = -2x represents a linear function, so its graph is a straight line with a slope of -2. The graph will have a negative slope and will slope downward from left to right.
On the other hand, the equation y = -x^2 represents a quadratic function, which is a parabola that opens downward. It is a symmetric U-shaped curve.
Therefore, the graphs are different in terms of their shape and behavior. One is a straight line, while the other is a curved parabola.