quadratics journal
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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:
Multiply a and c 1 x 8= 8
Find 2 numbers that multiply to that product and add to b
4 and 24 x 2= 84 + 2= 6
Put both numbers over a 4/1, 2/1
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
Multiply a and c 6 x 3= 18
Find 2 numbers that multiply to that product and add to b
2 and 92 x 9= 182 + 9= 11
Put both numbers over a 2/6, 9/6
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
a.
b.
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
Pick 3 points/Fill in for x
x y
-1 4
0 2
1 -4
Graph the parabola/reflect the points
Find x values to find solution About -2.4 and .4
Example 3
Set y =0
Make a t table
Find vertex
Pick 3 points/Fill in for x
x Y
2 1
0 5
-1 10
Graph the parabola/reflect the points
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
Make sure there is not an x by itself
No
Square root both sides and don’t forget the
x=
Example 3
Get by itself +2 +2 =16 =4
Make sure there is not an x by itself
No
Square root both sides and don’t forget the
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
Multiply a and c 5 x 3= 15
Find 2 numbers that multiply to that product and add to b
5 and 35 x 3=155 + 3=8
Put both numbers over a 5/8, 3/8
Reduce if possible Not possible
Make those two numbers negative
-5/8, -3/8
x=-5/8, -3/8
Example 2
Multiply a and c 4 x 6= 24
Find 2 numbers that multiply to that product and add to b
2 and 122 x 12= 242 + 12= 14
Put both numbers over a 2/4, 12/4
Reduce if possible 2/4= 1/212/4= 3
Make those two numbers negative
-1/2, -3
x= -1/2, -3
Example 3
Multiply a and c 2 x -3= -6
Find 2 numbers that multiply to that product and add to b
-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
Make those two numbers negative
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
Complete the square 6/2= 3
Add (b/2) to both sides
(x + 3) =17
Square root both sides x + 3=
Don’t forget the x= -3
Example 3
Get =1 + 2x= 6
Get c by itself + 2x= 6
Complete the square 2/2= 1
Add (b/2) to both sides
(x + 1) = 7
Square root both sides x + 1=
Don’t forget the x= -1
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
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