For instance, we have a quadratic inequality
y < -3x2 + 5 x + 8,
We use a simple formula –D /2 E to get value of x – coordinate of vertex. This Point would be the highest or lowest point. In case of our example we have D = -5 and E = -3. We will get -5 /2 (-3) = 5 /6.
Substitute the values of 'x' coordinate of vertex i.e. 1 to get corresponding value of 'y'. We get y = 145 /12 for x = 5 /6. Thus coordinates of our vertex are (5 /6, 145 /12).
Next we replace the inequality sign and put equality sign and making it equals to 0, we get equation of the form: 0 = -3x2 + 5 x + 8. Now we make use of Factorization method to find the solution of equation -3x2 + 5 x + 8 = 0. We get x = -1. Thus we get x- intercepts as: (8 /3, 0) and (-1, 0).
Draw the Parabola such that it passes through two x – intercepts and vertex. Use the dotted line to represent the curve. As original equation is having less than inequality, we shade the region below the line. Next we use x – intercepts and shaded region to determine the actual graph of inequality as -1 < x < 8 /3