# 3.3 Quadratic Equations and Inequalities.pdf - Name 3.3...

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Name: _________________________________ 1 3.3 Quadratic Equations and Inequalities Quadratic Equations and Factoring A quadratic equation is an equation that can be written in standard form as _______________________, where ? , ? , and ? are constants with ? ≠ 0 . Recall: the __________ of a function are all places where the function , i.e. the ___-coordinate, is ________. The solutions to a quadratic equation, also called ____________, represent the ________________________ of the graphed quadratic function. Quadratic equations can have ______ real solutions, ________ real solution, or ________ real solutions. Quadratic equations can be solved symbolically by a variety of methods: __________________, the ______________ __________ property, completing the square, and the ____________________ ______________. S TEPS TO S OLVE AN E QUATION BY F ACTORING : 1. G ET ________ ON ONE SIDE OF THE EQUATION . 2. ______________ THE EXPRESSION ON THE OTHER SIDE . 3. S ET EACH FACTOR EQUAL TO __________ AND ____________ FOR 𝑥 . Factoring is based on the __________-product property, which states that ?? = 0 if and only if __________ or __________ or ___________. It is important to remember that this property works only for _____! This is why your first step will always be to get ________ on one side! Concept Question: Give an example of an ? and ? where ?? = 1 but neither ? nor ? is equal to one (1). Then give an example where ? = 1 or ? = 1 but ?? ≠ 1 . Example 1 a) Solve 2𝑥 2 + 2𝑥 − 11 = 1

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Guided Notes 3.3 Quadratic Equations and Inequalities 2 b) Find all zeros of the function 𝑃(𝑥) = 𝑥 2 − 6𝑥 + 9 . c) Find the exact values for the 𝑥 -intercepts shown in the figure.

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