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Quadratic Equations Consider the following quadratic function and equation: What has changed between the two? The y has been replaced with the number 0. i. e. We are being asked to find the value of x when y=0. i. e. We are being asked to find the x-intercepts. A quadratic equation is essentially a question asking you to find the x-intercepts. We call this the solution, the roots, or the zeroes.

Solving Quadratic Equations 4 methods Method 1: Graphing Change equation to standard form. Now check your answer. x=1 or x=5 i. e. x=1, 5

Solving Quadratic Equations 4 methods Method 2: Completing the Square Change equation to standard form and solve the equation by isolating the variable. x=1 or x=5 i. e. x=1, 5

Solving Quadratic Equations 4 methods Method 3: Factoring Factor the equation and use the zero product principle (if a • b=0 then either a=0 or b=0) x=1 or x=5 i. e. x=1, 5

Solving Quadratic Equations 4 methods Method 4: The Quadratic Formula This formula can be derived by completing the square on x=1 or x=5 i. e. x=1, 5

Solving Quadratic Equations 4 methods It is important to be able to solve quadratics in all 4 methods. For some questions, it is easier to use one method over the other methods. For some questions, there will be only one method that works. Ex. Solve f(x) = 0 where f(x) is graphed below. x= -7 or x=2 i. e. x=-7, 2

Examples

Examples

Examples

Examples