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Unit 14: Quadratic functions & equations
About this unit.
We've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems.
Intro to parabolas
- Parabolas intro (Opens a modal)
- Interpreting a parabola in context (Opens a modal)
- Interpret a quadratic graph (Opens a modal)
- Parabolas intro Get 3 of 4 questions to level up!
- Interpret parabolas in context Get 3 of 4 questions to level up!
- Interpret a quadratic graph Get 3 of 4 questions to level up!
Solving and graphing with factored form
- Zero product property (Opens a modal)
- Graphing quadratics in factored form (Opens a modal)
- Quadratic word problems (factored form) (Opens a modal)
- Zero product property Get 3 of 4 questions to level up!
- Graph quadratics in factored form Get 3 of 4 questions to level up!
- Quadratic word problems (factored form) Get 3 of 4 questions to level up!
Solving by taking the square root
- Solving quadratics by taking square roots (Opens a modal)
- Solving quadratics by taking square roots examples (Opens a modal)
- Quadratics by taking square roots: strategy (Opens a modal)
- Solving quadratics by taking square roots: with steps (Opens a modal)
- Solving simple quadratics review (Opens a modal)
- Quadratics by taking square roots (intro) Get 3 of 4 questions to level up!
- Quadratics by taking square roots Get 3 of 4 questions to level up!
- Quadratics by taking square roots: strategy Get 3 of 4 questions to level up!
- Quadratics by taking square roots: with steps Get 3 of 4 questions to level up!
Vertex form
- Vertex form introduction (Opens a modal)
- Graphing quadratics: vertex form (Opens a modal)
- Quadratic word problems (vertex form) (Opens a modal)
- Graph quadratics in vertex form Get 3 of 4 questions to level up!
- Quadratic word problems (vertex form) Get 3 of 4 questions to level up!
Solving quadratics by factoring
- Solving quadratics by factoring (Opens a modal)
- Solving quadratics by factoring: leading coefficient ≠ 1 (Opens a modal)
- Solving quadratics using structure (Opens a modal)
- Quadratic equations word problem: triangle dimensions (Opens a modal)
- Quadratic equations word problem: box dimensions (Opens a modal)
- Solving quadratics by factoring review (Opens a modal)
- Quadratics by factoring (intro) Get 3 of 4 questions to level up!
- Quadratics by factoring Get 3 of 4 questions to level up!
- Solve equations using structure Get 3 of 4 questions to level up!
The quadratic formula
- The quadratic formula (Opens a modal)
- Understanding the quadratic formula (Opens a modal)
- Worked example: quadratic formula (example 2) (Opens a modal)
- Worked example: quadratic formula (negative coefficients) (Opens a modal)
- Using the quadratic formula: number of solutions (Opens a modal)
- Quadratic formula review (Opens a modal)
- Discriminant review (Opens a modal)
- Quadratic formula Get 3 of 4 questions to level up!
- Number of solutions of quadratic equations Get 3 of 4 questions to level up!
Completing the square intro
- Completing the square (Opens a modal)
- Worked example: Completing the square (intro) (Opens a modal)
- Worked example: Rewriting expressions by completing the square (Opens a modal)
- Worked example: Rewriting & solving equations by completing the square (Opens a modal)
- Completing the square (intro) Get 3 of 4 questions to level up!
- Completing the square (intermediate) Get 3 of 4 questions to level up!
More on completing the square
- Solve by completing the square: Integer solutions (Opens a modal)
- Solve by completing the square: Non-integer solutions (Opens a modal)
- Worked example: completing the square (leading coefficient ≠ 1) (Opens a modal)
- Solving quadratics by completing the square: no solution (Opens a modal)
- Proof of the quadratic formula (Opens a modal)
- Solving quadratics by completing the square (Opens a modal)
- Completing the square review (Opens a modal)
- Quadratic formula proof review (Opens a modal)
- Solve equations by completing the square Get 3 of 4 questions to level up!
- Completing the square Get 3 of 4 questions to level up!
Strategizing to solve quadratic equations
- Strategy in solving quadratic equations (Opens a modal)
- Strategy in solving quadratics Get 3 of 4 questions to level up!
Quadratic standard form
- Finding the vertex of a parabola in standard form (Opens a modal)
- Graphing quadratics: standard form (Opens a modal)
- Quadratic word problem: ball (Opens a modal)
- Graph quadratics in standard form Get 3 of 4 questions to level up!
- Quadratic word problems (standard form) Get 3 of 4 questions to level up!
Features & forms of quadratic functions
- Forms & features of quadratic functions (Opens a modal)
- Worked examples: Forms & features of quadratic functions (Opens a modal)
- Vertex & axis of symmetry of a parabola (Opens a modal)
- Finding features of quadratic functions (Opens a modal)
- Interpret quadratic models: Factored form (Opens a modal)
- Interpret quadratic models: Vertex form (Opens a modal)
- Graphing quadratics review (Opens a modal)
- Creativity break: How does creativity play a role in your everyday life? (Opens a modal)
- Features of quadratic functions: strategy Get 3 of 4 questions to level up!
- Features of quadratic functions Get 3 of 4 questions to level up!
- Graph parabolas in all forms Get 3 of 4 questions to level up!
- Interpret quadratic models Get 3 of 4 questions to level up!
Comparing quadratic functions
- Comparing features of quadratic functions (Opens a modal)
- Comparing maximum points of quadratic functions (Opens a modal)
- Compare quadratic functions Get 3 of 4 questions to level up!
Transforming quadratic functions
- Intro to parabola transformations (Opens a modal)
- Shifting parabolas (Opens a modal)
- Scaling & reflecting parabolas (Opens a modal)
- Quadratic functions & equations: FAQ (Opens a modal)
- Shift parabolas Get 3 of 4 questions to level up!
- Scale & reflect parabolas Get 3 of 4 questions to level up!
IMAGES
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The Algebra 1 Worksheets are randomly created and will never repeat so you have an endless supply of quality Algebra 1 Worksheets to use in the classroom or at home. We have twelve different topics covering Basic Skills, Domain and Range, Equations, Exponents, Inequalities, Linear Functions, Polynomials, Quadratic Functions, Radical Expressions ...
Infinite Algebra 1 covers all typical algebra material, over 90 topics in all, from adding and subtracting positives and negatives to solving rational equations. Suitable for any class with algebra content. ... Included in version 1.45 released 4/12/2011: New: Assignments from this program can be opened and modified by our other programs ...
Finding slope from a graph. Finding slope from two points. Finding slope from an equation. Graphing lines using slope-intercept form. Graphing lines using standard form. Writing linear equations. Graphing linear inequalities. Graphing absolute value equations. Direct variation.
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
Unit test. Level up on all the skills in this unit and collect up to 1,100 Mastery points! There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
Kuta Software - Infinite Algebra 1 Name_____ Solving Systems of Equations by Substitution Date_____ Period____ Solve each system by substitution. 1) y = 6x − 11 −2x − 3y = −7 (2, 1) 2) 2x − 3y = −1 y = x − 1 (4, 3) 3) y = −3x + 5 5x − 4y = −3 (1, 2) 4) −3x − 3y = 3 y = −5x − 17 (−4, 3)
19) 24 a − 22 = −4(1 − 6a) 20) −5(1 − 5x) + 5(−8x − 2) = −4x − 8x ©k l2t0 1K2 U KIu utua 7 qS7oCfOt BwMaDrlel uLxL5C8.h 4 2A aldl0 sr SibgOhct 7su Qrie XsZe6r zvPeBdB.V c HM9aJd Ie f Qwzihtdh b xINnNfAiVnBi3tSe g zAal 3g deVbXr3a D w1r.o Worksheet by Kuta Software LLC
Solve by completing the square: Integer solutions. (Opens a modal) Solve by completing the square: Non-integer solutions. (Opens a modal) Worked example: completing the square (leading coefficient ≠ 1) (Opens a modal) Solving quadratics by completing the square: no solution. (Opens a modal) Proof of the quadratic formula.
solve equations by adding or subtracting. • In Examples 1 and 2, students need to understand that solving an equation is a process of reasoning. In the process of learning to solve equations, students learn "if … then" statements as stated in the Properties of Equality such as if x = y, then x + 4 = y + 4. This understanding is key to ...
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. ©x d2Q0D1S2L RKcuptra2 GSRoYfRtDwWa8r9eb NLOL1Cs.j 4 lA0ll x TrCiagFhYtKsz OrVe4s4eTrTvXeZdy.c I RM8awd7e6 ywYiPtghR OItnLfpiqnAiutDeY QALlegpe6bSrIay V1g.N.
Infinite number of solutions. 23) −14 =. 24) (2, 0) (−1, 1) Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. ©q R2h041222 cK7uitqaL ASPovfPthwEanrQed vLOLrCy.6 w AAVlXl9 wrxivgghCtUsC xrmeAsfeGrivpe9du.Q Q iMwaHdMeB GwSijtZht xIrnOfNiRnFiotLeH 1AAlSgheWb4r0aG X1K.J.
Exercise 71. (9n + 5) − (3n − 7) = 20 − (4n − 2) Exercise 72. 2[ − 16 + 5(8k − 6)] = 8(3 − 4k) − 32. Answer. Classify Equations. In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. Exercise 73. 17y − 3(4 − 2y) = 11(y − 1) + 12y − 1.
Algebra 1 ID: 1 Name_____ Date_____ Period____ ©8 d2p0m1v4 0 YKmuHtSa P uS uo PfstYwpakr OeI YLpLdCm.E S WAll RlB zr Xi9gXh0tzsf mrWe5sEe Ar7vIe 6d i. 5 Solving One and Two Step Equations ... Solving One and Two Step Equations Solve each equation. 1) ...
Study with Quizlet and memorize flashcards containing terms like |x| = 3, |x + 5| = 12, |w - 8| = 20 and more.
Algebra 1 SOL A.4 Equations Worksheet Mrs. Grieser Translate the expressions and solve the resulting equation. 13) Ten times a number increased by 5 is 75. 14) The quotient of twice a number and 3 is 6. 15) Eight less than five times a number is 42. 16) The product of four and the quantity 2 less than a number is 16. Solve the word problems.
Section 2.2 : Linear Equations. Solve each of the following equations and check your answer. Here is a set of assignement problems (for use by instructors) to accompany the Linear Equations section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.
Algebra; Algebra questions and answers; b=16 Algebra 1 Assignment Solve each equation by factoring. 1) R² = 19 3) 2k² = -14 - 11k Solve each equation with the quadratic formula. 5) -6k² + 5k + 69 = 0 7) 9r² - 12r = 7 Sketch the graph of each function. 8) y = -2x² + 8x - 11 -63-4-3-2-1 Ay 1 2 3 Solve each equation with the quadratic formula.
Kuta Software - Infinite Algebra 1 Name_____ Solving Equations by Completing the Square Date_____ Period____ ... Solve each equation by completing the square. 1) a2 + 2a − 3 = 0 {1, −3} 2) a2 − 2a − 8 = 0 {4, −2} 3) p2 + 16 p − 22 = 0 {1.273 , −17.273} 4) k2 + 8k + 12 = 0 {−2, −6} 5) r2 + 2r − 33 = 0 {4.83 , −6.83} 6) a2 ...
D12 Unit 6 Algebra 1 Assignment All Methods of Solving Quadratics ... Solve each equation using factoring. 1) (2r - 7)(5r - 6) = 02) x2 + 7x + 10 = 0 3) x2 = 6x + 7 4) x2 - 4x = 0 Solve each equation by taking square roots. 5) 7r2 = 63 6) ... Infinite Algebra 1 - All Methods of Solving Quadratics
This assignment has three parts. Part 1. In the following chart, you will see multiple types of algebraic questions. You can use this Algebraic Equations lesson to refresh your memory on the most ...
Chapter 2 : Solving Equations and Inequalities. Here are a set of assignment problems for the Solving Equations and Inequalities chapter of the Algebra notes. Please note that these problems do not have any solutions available. These are intended mostly for instructors who might want a set of problems to assign for turning in.
In Exercises 1—6,solve the equation. Justify each step. Check your solution. 2. 5. The sum of the angle measures of a quadrilateral is 3600. In Exercises 7 and 8, write and solve an equation to find the value of x. Use a protractor to check the reasonableness of your answer. 7. 8. 1> In Exercises 9—14,solve the equation. Justify each step.
5. {−3} {. 7 2} {0} Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com.