Solve the quadratic inequality by locating the x-intercept(s) (if they exist), and noting the end behavior of the graph. Begin by writing the inequality in function form as needed.

Question

Answer 1

5x² ≥ 4x-4

x ≥ ±√[(4x-4)/4] ≥ ±√(x-1) For all x ≥ 0

Answer 2

First, solve for zero by subtracting 4x and adding 4. You should get

5x^2-4x+4 ≥ 0.

Now, if we find where this left-side expression is bigger than zero, it is equivalent to finding when 5x^2 is bigger than 4x-4.

Second, find out where the left-side 5x^2-4x+4 equals zero. You will get up to two values for x. They are called zeros or roots (two different names for the same thing). You can get that using the quadratic formula, which says

x=(-b ± √(b^2-4ac)) / (2a).

Third, find out if each interval (between the zeros) are bigger than zero or smaller than zero. You can do so by replacing x with values between the roots and see if you get a positive or negative number.

Give it a shot.