WARM UP What do you remember?...

QUADRATIC EQUATIONS SECTION 5.5

OBJECTIVES By the end of this part of the lesson, you should be able to… Simplify square roots. Solve quadratic equations by finding square roots.

SOLVING QUADRATIC EQUATIONS WITH SQUARE ROOTS If a quadratic equation is missing the b term we can solve using square roots. The goal is to get x by itself.

EXAMPLE 1: SIMPLIFYING RADICALS

EXAMPLE 2: SIMPLIFYING RADICALS

EXAMPLE 4: SOLVING BY FINDING SQUARE ROOTS Step 1) Rewrite in form ax 2 = c. Step 2) Isolate x 2. Step 3) Simplify. Step 4) Take the square root of each side.

EXAMPLE 5: SOLVING BY FINDING SQUARE ROOTS

EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS

OBJECTIVES By the end of today, you should be able to… Solve quadratic equations by factoring and graphing. What does it mean to solve an equation? Quick Review: When you solve an equation, you’re finding the values that make the statement true.

QUADRATIC EQUATIONS Remember - the standard form of a quadratic equation is ax 2 + bx + c = 0, where a ≠ 0. You can solve some quadratic equations in standard form by factoring the quadratic expression and then using… The Zero-Product Property!

THE ZERO-PRODUCT PROPERTY The Zero-Product Property helps us solve quadratic equations that have been factored. The Zero-Product Property states: If ab = 0, then a = 0 or b = 0. For example, if (x + 3)(x - 7)=0, then (x + 3) = 0 or (x - 7) = 0.

EXAMPLE 1: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

EXAMPLE 2: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

EXAMPLE 3: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

EXAMPLE 4: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. ???

SOLVING BY GRAPHING You can solve a quadratic equation in standard form by graphing its related quadratic function, y = ax 2 + bx +c and finding the x-intercepts. Quadratic equation cannot be solved by factoring Quadratic equation can be solved by graphing!

SOLVING BY GRAPHING 1)Write in standard form 2)Graph in your calculator 3)Find the x-intercepts

SOLVING BY GRAPHING EquationX-intercept(s) x 2 – 6x + 9 x 2 + 4x – 5

HOMEWORK Worksheet 5.5 #s 1, 3, 7, 11, 30, 34, 53, 60 Systems Projects – due Monday!