Final answer:
To find the x-intercepts of the equation y = x² - 5x, set y=0 and solve for x. The x-intercepts are x=0 and x=5. To test for symmetry, substitute -x for x in the equation and simplify. The graph is not symmetric about the y-axis.
Step-by-step explanation:
To find the x-intercepts of the given equation y = x² - 5x, we need to set y equal to zero and solve for x. So we have:
0 = x² - 5x
Using factoring, we can rewrite this equation as:
0 = x(x - 5)
So the x-intercepts are x = 0 and x = 5.
To test for symmetry, we can substitute -x for x in the equation and simplify. If the resulting expression is equal to the original equation, then the graph is symmetric about the y-axis. In this case, we have:
y = (-x)² - 5(-x)
Simplifying, we get:
y = x² + 5x
Since y = x² - 5x is not equal to y = x² + 5x, the graph is not symmetric about the y-axis.