Question

The graph of y=x^2-4x is shown on the grid. Find the range of values for which x^2-4x<0.

Answer 1

`\boxed{0} < x < \boxed{4}`

Explanation:

The graph is y = x² - 4x

For x² - 4x < 0 find out the interval of x
Factor x² - 4x ==> x(x - 4)

x² - 4x < 0 ==> x(x-4) < 0

Find the x-intercepts where x(x - 4) = 0

x(x - 4) = 0 means
x = 0 or x - 4 = 0
x - 4 = 0 ==> x = 4
These are critical points where the function changes sign

From the graph we see that the function has a value of 0 at x = 0 and x = 4 and is negative between 0 and 4

So the range of values for x where x² - 4x < 0 is

`\boxed{0} < x < \boxed{4}`

Hope that makes sense. If not, please ask questions