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# How to Do Graphing and Solving Quadratic Inequalities?

TopTo find the solution for a Quadratic Equation like Y = C X2 + D X + E, means to determine the values of intercepts that are made by equation on x – axis and its tip. Factorization technique is used for reducing the quadratic equation to its simplest form. A quadratic equation can also be solved by Graphing. Solving inequalities is different as compared to solving equalities. Let us learn how to do graphing and solving Quadratic Inequalities.
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