Solve Equations in Factored Form

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Presentation transcript:

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Vocabulary Zero-Product Property Let a and b be real numbers. If ab = 0, then = 0 or = 0. a b

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Example 1 Use the zero-product property Solve Write original equation. ______________ property. Zero-product x = ______ or x = _____ Solve for x. 5 and -4 The solutions of the equation are ______________. Check. Substitute each solution into the original equation to check.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Checkpoint. Complete the following exercises.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Methods of Factoring Binomial Trinomial 4 or more terms GCF GCF GCF Difference of Squares Perfect Square Trinomial Grouping Two Binomials (Shortcut) Two Binomials (cross)

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Example 2 Solve an equation by factoring Solve Write original equation. Factor left side. (GCF) Zero-product property. x = ______ or x = _____ Solve for x. 0 and -5 The solutions of the equation are ______________.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Example 3 Solve an equation by factoring Solve Write original equation. 24b Subtract _____ from each side. Factor left side. (GCF) Zero-product property. x = ______ or x = _____ Solve for b. 0 and 8/3 The solutions of the equation are ______________.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Example 3 Solve a multi-step problem Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground? Solution Step 1 Write a model for the water’s height above ground. Vertical motion model. v = ___ and s = ___. Simplify.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Example 3 Solve a multi-step problem Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground? Solution Step 2 Substitute __ for h. When the water lands, its height above the ground is __ feet. Solve for t. Substitute __ for h. Factor right side. Zero-product property. t = ______ or t = _____ Solve for x. 1.25 The water lands on the ground ______ after it is sprayed.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Checkpoint. Complete the following exercises.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Checkpoint. Complete the following exercises.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form Checkpoint. Complete the following exercises. In Example 4, suppose the initial velocity is 18 feet per second. After how many seconds does the water land on the ground? 1.125 The water lands on the ground ______ after it is sprayed.

Solve Equations in Factored Form 2.5 Solve Equations in Factored Form