Level 5 NZ Curriculum Achievement Objectives for Quadratics
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA 5-9: Relate simple quadratic relationships found in number and spatial patterns.
NA 5-9: Relate simple quadratic relationships found in number and spatial patterns.
In this unit you will learn:
1) What is a quadratic pattern
2) Expanding Two Brackets
3) Factorizing Quadratics
4) Solving Quadratic Equations
5) Determine whether a pattern is linear, quadratic or neither
6) Graphing quadratics
1) What is a quadratic pattern
2) Expanding Two Brackets
3) Factorizing Quadratics
4) Solving Quadratic Equations
5) Determine whether a pattern is linear, quadratic or neither
6) Graphing quadratics
1) What is a quadratic pattern
A quadratic pattern is represented by an equation that has two x's. This can be written as:
2) Expanding Two Brackets
When we expand to brackets, we must make sure that everything in the first bracket is multiplied by everything in the second bracket. We will then get four terms and then we must simplify is possible (collect any like terms together).
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Check out these websites for some more help:
www.bbc.co.uk/schools/gcsebitesize/maths/algebra/symbolsrev5.shtml
http://www.maths.com/algebra/expand-brackets/one-set-of-double-brackets/index.htm
www.bbc.co.uk/schools/gcsebitesize/maths/algebra/symbolsrev5.shtml
http://www.maths.com/algebra/expand-brackets/one-set-of-double-brackets/index.htm
Homework
algebra-expanding-two-brackets_homework_answers.pdf | |
File Size: | 199 kb |
File Type: |
3) Factorising Quadratics
To factorize means to split up an expression into two or more terms that are being multiplied.
When we factorize a quadratic, we are splitting it up into two brackets so when they are expanded, they give us the original expression.
When we factorize a quadratic, we are splitting it up into two brackets so when they are expanded, they give us the original expression.
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Check out these websites for some more help:
www.purplemath.com/modules/factquad.htm
http://studymaths.co.uk/topics/factorisingQuadraticExpressions.php
www.purplemath.com/modules/factquad.htm
http://studymaths.co.uk/topics/factorisingQuadraticExpressions.php
Homework
factorising-quadratics-answers_homework.pdf | |
File Size: | 129 kb |
File Type: |
4) Solving Quadratic Equations
Follow the steps below to solve a quadratic equation:
1) Ensure the equation equals zero. If not, rearrange it so it does.
2) Factorise the equation if it isn't factorised.
3) Set each factor equal to zero.
4) Solve for each factor.
THERE WILL ALWAYS BE TWO ANSWERS!!!
1) Ensure the equation equals zero. If not, rearrange it so it does.
2) Factorise the equation if it isn't factorised.
3) Set each factor equal to zero.
4) Solve for each factor.
THERE WILL ALWAYS BE TWO ANSWERS!!!
Homework
solving_quadratic_equations__b___by_factorising_._answers_homework.pdf | |
File Size: | 203 kb |
File Type: |
Check out these websites:
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/square-roots-and-factoring/factoring/solve-by-factoring
http://www.coolmath.com/algebra/09-solving-quadratics/02-solving-quadratic-equations-by-factoring-03
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/square-roots-and-factoring/factoring/solve-by-factoring
http://www.coolmath.com/algebra/09-solving-quadratics/02-solving-quadratic-equations-by-factoring-03
5) Determining the Pattern (Linear, Quadratic or Neither)
We can determine what type of pattern we have by examining three aspects:
1) The Equation
2) Table of Values
3) The Graph
1) The Equation
2) Table of Values
3) The Graph
LINEAR PATTERNS:
1) The equation has an x and/or a y. The highest power is 1.
eg) y = 2x + 3
y = x
2y = 5x - 1
x = 3
y = -5
2) The "y'" column in a table of values increases / decreases by the same amount"
1) The equation has an x and/or a y. The highest power is 1.
eg) y = 2x + 3
y = x
2y = 5x - 1
x = 3
y = -5
2) The "y'" column in a table of values increases / decreases by the same amount"
eg) In the table to the below, the value of y is increasing by 8 each time.