College Prep Unit 9: Quadratic Functions College Prep
Transcript of College Prep Unit 9: Quadratic Functions College Prep
College Prep Unit 9: Quadratic Functions
Ms. Talhami 1
College Prep Unit 9: Quadratic Functions
Name_________________
College Prep Unit 9: Quadratic Functions
Ms. Talhami 2
Helpful Vocabulary Word Definition/Explanation Examples/Helpful Tips
College Prep Unit 9: Quadratic Functions
Ms. Talhami 3
What is a Quadratic Function? Basic Form Standard Form
What does the graph of a quadratic function look like? This shape is called a _______________.
Axis of Symmetry (Line)
Vertex (Turning Point)
College Prep Unit 9: Quadratic Functions
Ms. Talhami 4
For each of the following parabolas, find the axis of symmetry and the vertex.
AOS:__________ Vertex:__________
AOS:__________ Vertex:__________
AOS:__________ Vertex:__________
AOS:__________ Vertex:__________
AOS:__________ Vertex:__________
AOS:__________ Vertex:__________
College Prep Unit 9: Quadratic Functions
Ms. Talhami 5
Standard Form vs Vertex Form Standard Form Vertex Form
How does changing the value of βaβ change the graph?
Therefore as |π| increases, the graph becomes _______________.
Therefore as |π| decreases, the graph becomes _______________.
And if π is negative, the graph ________________________________________. How does changing the value of βcβ (which is βkβ in vertex form) change the graph?
Therefore if π is positive, the graph _______________ π units.
Therefore if π is negative, the graph _______________ π units.
Parent Function
π¦ = π₯!
π¦ = 2π₯!
π¦ =12π₯!
Parent Function
π¦ = π₯!
π¦ = π₯! + 3
π¦ = π₯! β 2
College Prep Unit 9: Quadratic Functions
Ms. Talhami 6
How does changing the value of βhβ change the graph?
Therefore if β is positive, the graph _______________ β units.
Therefore if β is negative, the graph _______________ β units. Do not use a calculator. Graph the following. Describe the transformations. You must plot and state the 3 βkeyβ points, wherever they end up after transformation. 1. π(π₯) = β(π₯ + 1)! + 4 2. π¦ = (π₯ β 3)!
3. π(π₯) = β(π₯ + 4)! β 2 4. π¦ = 2π₯! β 5
Parent Function
π¦ = π₯!
π¦ = (π₯ β 2)!
π¦ = (π₯ + 4)!
College Prep Unit 9: Quadratic Functions
Ms. Talhami 7
5. π(π₯) = "!(π₯ β 2)! 6. π¦ = β3(π₯ β 1)! + 6
Write the quadratic equation, in vertex form for each graph. 7. ____________________ 8. ____________________
9. ____________________ 10. ____________________
College Prep Unit 9: Quadratic Functions
Ms. Talhami 8
11. ____________________ 12. ____________________
How to Graph Using the Axis of Symmetry, the Vertex, and the Intercepts
Steps to Sketch the Graph the Quadratic Function π¦ = ππ₯! + ππ₯ + π 1. Determinewhethertheparabolaopensupwardordownward.
Ifπ > 0,itopensupward.Ifπ < 0,itopensdownward.
2. Graphtheaxisofsymmetry,π₯ = β !"#
3. Plotthevertex,$β !"#, π 'β !
"#()
4. Determineanyx-interceptsandplotthecorrespondingpoints.Anx-interceptisasolutiontotheequationππ₯! + ππ₯ + π = 0.
5. Determinethey-intercept,c,andplotthecorrespondingpoint.Thenusesymmetrytoplottheimageofthepoint(0, π).
6. Connectthepointswithasmoothcurve. Sketch the following graphs: 1. π¦ = π₯! β 2π₯ β 3 2. π¦ = β2π₯! + 2π₯
College Prep Unit 9: Quadratic Functions
Ms. Talhami 9
3. π¦ = 3π₯! β 2π₯ β 1 4. π¦ = β2π₯! β 4π₯
Letβs Review Factoring Quadratics Solve the following by factoring (if factorable): 1. π₯! + 10π₯ β 11 = 0 2. π₯! β 12π₯ + 7 = 0 Standard Form and Perfect Square Trinomials
1. (x β 2)2 a = ______ b= ______ c= ______
2. (x + 5)2 a = ______ b= ______ c= ______
3. (x β 9)2 a = ______ b= ______ c= ______
Completing the Square
Determine the value of the constant term, c, to create a perfect square trinomial then write the trinomial in factored form. 1.
x2 + 4x + ___ Factored Form _____________
2. x2 + 10x + ___
Factored Form _____________
3. x2 + 14x + ___
Factored Form _____________
4. x2 β 12x + ___
Factored Form _____________
5. x2 β 8x + ___
Factored Form _____________
6. x2 β 2x + ___
Factored Form _____________
College Prep Unit 9: Quadratic Functions
Ms. Talhami 10
Using Completing the Square with Quadratic Equations to Rewrite from Standard Form to Vertex Form 1.
x2 + 6x + 3 = 0
2. x2 + 10x + 20 = 0
3. x2 β 8x β 3 = 0
How to Solve Quadratics (where π = 1 and solutions are real numbers) by Completing the Square 1. π₯! + 10π₯ β 11 = 0 2. π₯! β 12π₯ + 7 = 0 3. π₯! + 14π₯ β 51 = 0 4. π₯! = 2π₯ + 3 5. π₯! + 14π₯ = 48 6. β49 = βπ₯! + 6π₯ 7. π₯! β 48 = 14π₯ 8. π₯! + 6π₯ β 49 = 0
College Prep Unit 9: Quadratic Functions
Ms. Talhami 11
How to Solve Quadratics (where π β 1 and solutions are imaginary) by Completing the Square 1. 5π₯! + 20π₯ β 60 = 0 2. 8π₯! + 16π₯ β 42 = 0 3. π₯! β 6π₯ = β91 4. 2π₯! β 3π₯ β 11 = 0 5. π₯! + 6π₯ + 41 = 0 6. 3π₯! = β4 + 8π₯ Another Method to Solving Quadratics If the quadratic equation is written in standard form, you can use the quadratic formula to solve for the roots.
π₯ =βπ Β± βπ" β 4ππ
2π
Examples 1. 2π₯! + 5π₯ β 7 = 0 2. 4π₯! β 8π₯ + 13 = 0 3. π₯! + 4π₯ β 14 = 0
College Prep Unit 9: Quadratic Functions
Ms. Talhami 12
Practice Solving Quadratics Using the Quadratic Formula
Β©n C2v0Z1q2v wKzu2t8az aSPopfptvwDaAruet FLKLfC2.S s KANltlH trIiAgPhKtJsI prgeFsXeQrJv9e8dM.E F fMOavdqe7 fwxintLhg DI0nIfgiRnui2tgeQ OAKlMgdecb0rBa9 01i.I Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Using the Quadratic Formula
Solve each equation with the quadratic formula.
1)
m2 β 5
m β 14 = 0 2)
b2 β 4
b + 4 = 0
3)
2
m2 + 2
m β 12 = 0 4)
2
x2 β 3
x β 5 = 0
5)
x2 + 4
x + 3 = 0 6)
2
x2 + 3
x β 20 = 0
7)
4
b2 + 8
b + 7 = 4 8)
2
m2 β 7
m β 13 = β10
-1-