quadratics journal

Quadratics Journal

Salvador Amaya

Find a GCF if possible Divide the whole equation by GCF Multiply a and c Find 2 numbers that multiply to that product

and add to b Put both numbers over a Reduce if possible

How to factor a polynomial

Example 1

Find a GCF if possible No GCF

Divide by GCF No GCF

Multiply a and c 2 x 12= 24

Find 2 numbers that multiply to that product and add to b

8 and 38 x 3= 248 + 3= 11

Put both numbers over a 8/2, 3/2

Reduce if possible 8/2= 43/2 can’t be reduced so it stays as 3/2

Factors of are 4 and 3/2

Example 2

Find GCF if possible GCF=2

Divide the whole equation by GCF.

Divide by 2 all. New equation:



4 and 24 x 2= 84 + 2= 6


Reduce if possible 4/1= 42/1= 2

Factor of are 4 and 2.

Example 3

Find GCF if possible No GCF

Divide the whole equation by GCF

No GCF



2 and 92 x 9= 182 + 9= 11


Reduce if possible 2/6= 1/39/6= 3/2

Factors of are 1/3 and 3/2

An equation with an squared number a can’t equal 0 (if it does then it is a linear

function It is a parabola when graphed. In the form of:

What is a quadratic funtion?

A linear graphs a line, a quadratic a parabola

A linear is in form y=mx+b, a quadratic in

In a linear function, the y and x don’t have powers

Difference between linear

Is this a quadratic or linear function? Why?

Example 1

It is a linear equation It has no powers It is in form y=mx+b When graphed it is a line:

Which of these equations graphs a parabola?

a.

b.

c.

Example 2

It is c.

c.

Which equation is quadratic?

Example 3

Because it has powers on x.

It is

Convert, if not already, to graphing form:

A changes the steepness of parabola If a<0, the parabola goes down of vertex, and is

wide If a>0, the parabola goes up of vertex, and is thin B moves right or left the parabola vertex If b is +, vertex goes in the negative side If b is -, vertex goes in positive side C moves vertex up or down. +c moves up -c moves down

How to graph a quadratic function

It will graph: thin, it goes up of vertex, vertex is in -3 in x, and it is in -5 in y

Example 1

It will graph wide, it goes down of vertex, vertex is in -8 in x, and it is in 1 in y

Example 2

It will graph wide, it goes down of vertex, vertex is in 5 in c, and it is in -6 in y

Example 3

Set y=0 Graph the function

◦ Make a t-table◦ Find the vertex using the formula x=-b/2a◦ Pick 3 points in one side of vertex◦ Fill in for x in the function to figure out y◦ Graph the parabola◦ Reflect the points on the other side of the vertex

Find the x-values where it crosses the x-axis.(solution)

No crossing x-axis=no solution

Solve by graphing

It is the number or numbers that fill in for x for the equation to equal 0

Solution

Set y =0

Make a t table

Find vertex

Pick 3 points/Fill in for x

Example 1

x y

-1 2

0 3

1 6

2 11

Graph the parabola/reflect the points

Find x values to find solution No solution

Example 2

Set y =0

Make a t table

Find vertex


x y

-1 4

0 2

1 -4


Find x values to find solution About -2.4 and .4

Example 3

Set y =0

Make a t table

Find vertex


x Y

2 1

0 5

-1 10


Find x values to find solution No solution

Get by itself Make sure there is not an x by itself Square root both sides and don’t forget the

Solve by square roots

Example 1

Get by itself -9 -9 =9 =3

Make sure there is not an x by itself

No

Square root both sides and don’t forget the

x=

Example 2

Get by itself -4 -4 =12

=6


No


x=

Example 3

Get by itself +2 +2 =16 =4


No


x= 2

Multiply a and c Find 2 numbers that multiply to that product

and add to b Put both numbers over a Reduce if possible Make those two numbers negative

Solve by factoring

Example 1



5 and 35 x 3=155 + 3=8


Reduce if possible Not possible

Make those two numbers negative

-5/8, -3/8

x=-5/8, -3/8

Example 2



2 and 122 x 12= 242 + 12= 14


Reduce if possible 2/4= 1/212/4= 3


-1/2, -3

x= -1/2, -3

Example 3

Multiply a and c 2 x -3= -6


-6 and 1-6 x 1= -6-6 + 1= -5

Put both numbers over a -6/2, -5/2

Reduce if possible -6/2= -3½ can’t be reduced so it stays as 1/2


3, -1/2

x= 3, 5/2

Get a=1 Find b Divide b by 2 Square it Factor (x + b/2)

Complete the square

Get =1 Get c by itself Complete the square Add (b/2) to both sides Square root both sides Don’t forget the

Solve completing the square

Example 1

Get =1 + 4x + 1= 2

Get c by itself + 4x= 1

Complete the square 4/2= 2

Add (b/2) to both sides

(x + 2) =5

Square root both sides x + 2=

Don’t forget the x= -2

Example 2

Get =1 - 6x= 2

Get c by itself - 6x= 2



(x + 3) =17



Example 3

Get =1 + 2x= 6

Get c by itself + 2x= 6



(x + 1) = 7



Formula:

Solve with quadratic formula

It is the number that appears inside the square root in a quadratic equation.

Ex:

Discriminant

Discriminant

Example 1

x= -9/2

Example 2

Example 3

Geometry Review of Algebra Journal

In your own words respond to the following: Describe how to Factor any polynomial. Give at least 3 examples. _____(0-10 pts) Describe what at quadratic function is. Explain how to tell the difference between a quadratic function and a linear function. Give at least 3 examples. _____(0-10 pts) Describe how to graph a quadratic function. Include a discussion about maximum values, minimum values and vertices. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation by graphing it. What is a solution? Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using square roots. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using factoring. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using Completing the square. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using the Quadratic formula. Explain what a discriminant is. Give at least 3 examples. _____(0-5 pts) Neatness and originality bonus

quadratics journal

Documents

formula x

x dont

x xy2105

pointsfind x values

y example

form y

quadratic function

solutionset y