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Quadratic equation is very common in algebra. Quadratic means square. The equation which has the highest degree for the variable as two is called a quadratic equation. So the degree of the polynomial for a quadratic equation is always 2. The general form of a quadratic equation is ax2 + b x + c = 0. Here x is the unknown variable and a. b. c are the constants. The sign of the variable ‘a’ decides if the graph of the quadratic equation is upward or downward. The quadratic equation needs to be solved to graph it.

Example 1: Graph the quadratic equation x2 + 4x + 4.

Solution: Given here is the quadratic equation x2 + 4x + 4.

The first step is to solve for the quadratic equation.

The equation can be written as x2 + 2x + 2x + 4

Now factoring the common terms gives x(x + 2) + 2(x + 2) = 0.

Hence (x + 2) (x + 2) = 0

Therefor x = 2 is the solution.

Example 2: Graph the quadratic equation x2 + 5x + 6.

Solution: Given here is the quadratic equation x2 + 5x + 6.

The first step is to solve for the quadratic equation.

The equation can be written as x2 + 3x + 2x + 6

Now factoring the common terms gives x(x + 3) + 2(x + 3) = 0.

Hence (x + 3) (x + 2) = 0

Therefor x = -3, - 2 are the solutions.

The graph of the quadratic equations is given below.