Quadratic Functions and Equations Chapter 4 Quadratic Functions and Equations

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

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)

4.1 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 -

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

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

4.2 Standard Form of a Quadratic Function

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)

4.3 Modeling With Quadratic Functions Pg. 209-214 Obj: Learn how to model date with quadratic functions. F.IF.5, F.IF.4

4.4 Factoring Quadratic Expressions Pg. 216-223 Obj: Learn how to find common and binomial factors of quadratic expressions and factor special quadratic expressions. A.SSE.2

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

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

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

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.

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

4.6 Completing the Square Completing the Square

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

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

4.7 The Quadratic Formula The Quadratic Formula

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

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

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

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

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

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