Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)
y = 5x2 − 5x
the equation is y =5x^2-5x, not y = 5x2 − 5x
5x^2-5x = 0
5x(x-1) = 0
so, ...
the answer would be
x=0,x=1.
To find the x-intercepts of the parabola given by the equation, we need to set y equal to zero and solve for x. The x-intercepts are the points where the graph of the parabola intersects the x-axis.
Let's set y = 0 in the equation y = 5x^2 - 5x:
0 = 5x^2 - 5x
Now we can factor out common terms:
0 = 5x(x - 1)
Now, we have two possibilities for the equation to be equal to zero:
1) 5x = 0
This gives us x = 0
2) x - 1 = 0
This gives us x = 1
So, the x-intercepts of the parabola are x = 0 and x = 1.