Chapter 3 ReviewQuadratic Equations

Properties of Quadratics (Parabolas)direction of opening: if a parabola

opens up it has a U-shape, down it has a upside down U- shape.

vertex: the highest / lowest point on the parabola

axis of symmetry: the line of symmetry on the parabola this vertical line passes though the vertex

zeros/roots: the point(s) where the parabola passes through the x-axis

Example:

The direction of opening ______The vertex is (____, ____)The axis of symmetry is x = ______The zeros are (____, ____) and (____, ____)

Different Forms of the Parabola EquationsFACTORED STANDARD VERTEX

FORM FORM FORM

s and t are zeros a is the direction vertex is (h,k)

a is direction of of opening a is direction of opening opening

Expand

Factor

))(( txsxay cbxaxy 2

Complete the Square

Expand

khxay 2)(

ExpandingMultiply everything in one bracket by

everything in another.Example 1 Example 2

28136

282186

)43)(72(

2

2

xx

xxx

xx

123018

)4106(3

)41226(3

)13)(42(3

2

2

2

xx

xx

xxx

xx

FactoringTechnique 1:

Common FactoringTechnique 2:

Simple Trinomial

)72(3

3x is GCF

an x have and 3

by divisable are termsall

216 2

xx

xx

)4)(2(

842

642

86

1 is xoffront in number 2

2

xx

xx

Technique 3: Decomposition

Technique 4: Diff of Squares

)12)(3(

)3(1)3(2

3162

616

516

352

1not is xoffront in number

2

2

2

xx

xxx

xxx

xx

)32)(32(

39

24

94

subtracted being are and

squareperfect are both terms

2

2

xx

xx

x

Finding the VertexMethod 1: Calculate the zeros, axis, vertexExampleDetermine the vertex , use this information to

graph

Factor (if necessary)

to get equation into factored form

If equation is already factored skip this step

)4)(52(

)4(5)4(2

20582

4058

358

2032

2

2

xxy

xxxy

xxxy

xxy

4

3

242

5

42

5

40520

)4)(52(0

x

x

SYMMETRYOFAXIS

xORx

xORx

xx

ZEROSSet each term equal to zero and solve to get the zeros

Calculate the axis by adding the zeros and then dividing by 2

8169

16338

20)43(3)4

3(2 2

y

y

VERTEX

8

169,

4

3

Vertex is

Sub the axis into the equation to get the y-coordinate of the vertex

Chapter 3 Review QuestionsExpand and simplify quadratic equations - Ch. review p.330, #11 & Ch. review test p.337,#5Identify whether a relationship is linear or quadratic – Ch. review p.323, #1-3, p.326, #4-6 & Ch. review test p.337#1Find the common factors of an equation - Ch. review p.332,#14,15 & Ch. review test p.337#6Factor an equation in form - Ch. review p. p.332,#14,15 & Ch. review test p.337,#6Factor an equation in form - Ch. Rev.p. p.332,#14,15 & Ch. R.Tst p.337#6Solve an equation in form (finding the zeros) - Ch. review p.335,#16-20Solve an equation in form (finding the zeros) - Ch. review p.335#16-20 & Ch. review test p.338,#7Find factored form quadratic equations given roots and optimal values – Ch. review p.326,#4-6, p.329,#8-10, p.331,#12-13 & Ch. review test p.337,#3Solving word problems using quadratic equations or questions and word problems, find zeros, values of x for diff. events and optimal value & graph/interpret graphs & find equationsCh. review p.326,#4-6, p.329,#8-10, p.331,#12-13 & Ch. review test p.338,#8-10 & p.429#3,4Graph using transformations relative to (which has vertex (0,0)Ch. review p.418# 1-5, p.421,#6-8 & Ch. review test p.p.429#1,2,5Solve a word problem where I am asked to find the maximum, minimum or optimum value, given information to set-up the quadratic in factored, expanded form y=(x-s)(x-t)Ch. review p.423,#10&11,p.424#12-14 & Ch. review test p.429#6-7Solve a word problem where I am asked to find what x value will give me a given y value given information to set-up the quadratic in factored or expanded form y=(x-s)(x-t) - Ch. review p.427,#15-19