1. Quadratic Functions and Equations
Chapter 4
Quadratic Functions and Equations

2. 4.1 Quadratic Functions and Transformations
Pg. 194 – 201
Obj: Learn how to identify and graph quadratic functions.
F.BF.3, A.CED.1, F.IF.4, F.IF.6

3. 4.1 Quadratic Functions and Transformations
Parabola – the graph of a quadratic function
Quadratic Function – an equation that has a degree 2
Vertex Form –
Axis of Symmetry – a line that divides the parabola into two mirror images – x=h
Vertex of the Parabola –the intersection of the parabola and its axis of symmetry – (h,k)

4. 4.1 Quadratic Functions and Transformations
Minimum Value – the y-coordinate of the vertex, if a>0 – the parabola opens upward
Maximum Value – the y-coordinate of the vertex, if a <0 – the parabola opens downward
Parent Quadratic Function -

5. 4.1 Quadratic Functions and Transformations
Reflection, Stretch, and Compression
Reflection – a and –a
Stretch – a>1
Compression – 0<a<1
Translation of the Parabola
Horizontal – y=(x-h)² - move |h| units
Vertical – y=x²+k – move |k| units
Horizontal and Vertical – y=(x-h)²+k – move |h| units and |k| units

6. 4.2 Standard Form of a Quadratic Function
Pg. 202 – 208
Obj: Learn how to graph quadratic functions written in standard form.
A.CED.2, F.IF.4, F.IF.6, F.IF.8, F.IF.9

7. 4.2 Standard Form of a Quadratic Function

8. 4.2 Standard Form of a Quadratic Function
Properties of a Quadratic Function
If a>0, the parabola opens upward. If a<0, the parabola opens downward.
The axis of symmetry is x=-b/2a
Vertex (-b/2a, f(-b/2a))
Y-intercept (0,c)

9. 4.3 Modeling With Quadratic FunctionsPg
Obj: Learn how to model date with quadratic functions.
F.IF.5, F.IF.4

10. 4.4 Factoring Quadratic ExpressionsPg
Obj: Learn how to find common and binomial factors of quadratic expressions and factor special quadratic expressions.
A.SSE.2

11. 4.4 Factoring Quadratic Expressions
Factoring – rewriting an expression as a product of its factors
Greatest Common Factor (GCF) of an Expression – a common factor of the terms in the expression – the common factor with the greatest coefficient and the greatest exponent

12. 4.4 Factoring Quadratic Expressions
Perfect Square Trinomial – a trinomial that is the square of a binomial
Difference of Two Squares -

13. 4.5 Quadratic Equations Pg. 226-231
Obj: Learn how to solve quadratic equations by factoring and graphing.
A.CED.1, A.APR.3, A.SSE.1.a

14. 4.5 Quadratic Equations
Zero of a Function – where the graph of a function intersects the x-axis
Zero-Product Property – If ab=0, then a=0 or b=0.

15. 4.6 Completing the Square Pg. 233 – 239
Obj: Learn how to solve equations by completing the square and rewrite functions by completing the square.
A.REI.4.b

16. 4.6 Completing the Square
Completing the Square

17. 4.6 Completing the Square Solving an Equation by Completing the Square
Rewrite the equation in the form x²+bx=c
Complete the square by adding (b/2)² to each side of the equation.
Factor the trinomial
Find square roots
Solve for x

18. 4.7 The Quadratic Formula Pg. 240-247
Obj: Learn how to solve quadratic equations using the Quadratic Formula and determine the number of solutions by using the discriminant.
A.REI.4.b

19. 4.7 The Quadratic Formula
The Quadratic Formula

20. 4.7 The Quadratic Formula Discriminant b²-4ac Positive – two solutions
Zero – one real solution
Negative – no real solution

21. 4.8 Complex Numbers
Pg. 248 – 255
Obj: Learn how to identify, graph, and perform operations with complex numbers. Learn how to find complex number solutions of quadratic equations.
N.CN.1, N.CN.2, N.CN.7, N.CN.8

22. 4.8 Complex Numbers
Imaginary Unit – i the complex number whose square is -1
Imaginary Number – any number of the form a + bi
Complex Number – a + bi, where a and b are real numbers
Pure Imaginary Number – bi
Complex Number Plane – real axis and imaginary axis

23. 4.8 Complex Numbers
Absolute Value of a Complex Number – its distance from the origin in the complex plane
Complex Conjugates
a + bi
a - bi

24. 4.9 Quadratic Systems
Pg. 258 – 264
Obj: Learn how to solve and graph systems of linear and quadratic equations.
A.CED.3, A.REI.7, A.REI.11

25. 4.9 Quadratic Systems Solutions of a Linear-Quadratic System
Two Solutions
One Solution
No Solution