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 thatcan be written in the formThis 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 thefunction. (x-intercept meaning when the y=0)

0.a where ,0cbxax 2

Problem 1: Solving by graphing

What are the solutions of each equation?

Graph 1xy 2

01x c) 0x b) 01x)a 222

2xy 1xy 2

solution. number

real not isThere

0. solution,

one isThere

1. solutions

twoare There

Problem 2: Solving using the square root.

What are the solutions of ? 075x3 2 075x3 2 75x3 2 25x 2

25x

5x

Isolate the x in one side

Find the square root of each side and simplify

Your turn: 1616c)4d 015b)3x 036m)a 222

Answers6x

solution no 0

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?

l

w

h=3ft

V=l.w.h w3w2420

2w6420 2w70

w70

4.8366600265.8 The tank cannot be a negative width so onlythe positive root make sense.The tank will have a width of 8.4 ft

Answer

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?

015x8x 2 05x3x

05x or 03x

-5x -3x

Factor

Zero Property 0b or 0a0ab

Solve it

Your turn

018a15a2)c

020pp)b

014m5m)a

2

2

2

Answer

7,2)a

4,5)b

6,2

3)c

Problem 5: Writing the Standard Form First.

What are the solutions of ?18x21x4 2

018x21x4 2

06x3x4

06-x or 03x4

6x 4

3-x

Make the equation =0

Factor

Zero Property

Solve for x

Your turn

49x14x 2 Answer -7

Problem 6: Using Factoring to Solve a Real World Problem

17 in

x x

x

x

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 theframe and photo to be 315 sq. in. Whatshould the outer dimensions of the frame be? 11inlwA

17x211x2315

187x56x4315 2 128x56x40 2

32x14x40 2 2x16x40

02-x or 016x

2x -16x

Substitute

Make equation equals to zero

GCF: 4

Factor

Solve for x

Reasonable solution is x=2

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 evenTB pgs.551-552 exercises 8-54 pgs. 558-559 exercises 8-41