Solving Quadratic Equations.

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Presentation transcript:

Solving Quadratic Equations. Factoring to Solve Quadratic Equations What you’ll learn To solve quadratic equations by graphing and using square roots. To solve quadratic equations by factoring. Vocabulary Quadratic equation, Standard form of a quadratic equation, Zero of a function, Zero product property.

 Take a note: A quadratic equation is an equation that can be written in the form This form is called the standard form of a quadratic equation. The solution of a quadratic equation and the x-intercepts of the graph of the related function are often called roots of the equation or zeros of the function. (x-intercept meaning when the y=0) 

Problem 1: Solving by graphing What are the solutions of each equation? Graph

Problem 2: Solving using the square root. What are the solutions of ? Isolate the x in one side Find the square root of each side and simplify Your turn: Answers

V=l.w.h w l h=3ft Problem 3: An aquarium is designing a new exhibit to showcase tropical fish. The exhibit will include a tank that is rectangular prism with length l that is twice the with w. The volume of the tank is 420 cubic ft. What is the width of the tank to the nearest foot? w Answer V=l.w.h h=3ft l The tank cannot be a negative width so only the positive root make sense. The tank will have a width of 8.4 ft

Your turn: Suppose the tank in problem 3 will have a height of 4 ft. and a volume of 500 cubic feet. What is the width of the tank to the nearest tenth of a foot? Answer: 7.9 ft.

Problem 4: Using the Zero Property after factoring. What are the solutions of the equation? Factor Zero Property Solve it Your turn Answer

Problem 5: Writing the Standard Form First. What are the solutions of ? Make the equation =0 Factor Zero Property Solve for x Your turn Answer -7

Problem 6: Using Factoring to Solve a Real World Problem You are constructing a frame for the rectangular photo shown. You want the frame to be the same width all the way around and the total area of the frame and photo to be 315 sq. in. What should the outer dimensions of the frame be? x x x 11in Substitute 17 in Make equation equals to zero x GCF: 4 Reasonable solution is x=2 Factor Solve for x

Quiz @ HOME From the text book go to page 559 and in a piece of paper do exercises 46-50. Show me the work!!!!!!

Classwork odd Homework even TB pgs.551-552 exercises 8-54 pgs. 558-559 exercises 8-41