QUADRATIC FUNCTIONS
Unit Plan: Schedule, Quizzes and Exam Dates
2023 Assessments:
- Identifying characteristics of quadratic functions (domain/range, intercepts, vertex)
- Solve problems using characteristics of quadratic functions.
Unit Plan: Schedule, Quizzes and Exam Dates
2023 Assessments:
- Quiz 1A key and Quiz 1B key
- Quiz 2A key and Quiz 2Bkey
Properties of Quadratics: general format y=ax^2+bx+c
- Find the x-intercepts - the points on the x-axis and where y=0.
- Find the y-intercept - the point on the y-axis and where x=0.
- Vertex - the lowest or highest point on the function; where the graph and axis of symmetry meet.
- Axis of Symmetry - the equation (vertical line of x= ) that divides the function in to equal halves.
Lesson:
- Properties of Quadratic Functions
- Notes and Examples
- Calculator Instruction sheets
More Quadratic Properties:
- Domain: the x-values of the function.
- Range: the y-values of the function.
Lesson:
Calculator Skills
- Find maximum or minimum values.
- Find 'zeros' or 'roots' of functions.
- Use Trace or Table to find points on the functions
- Find equations using Regressions (enter data into two lists).
- Intersection - find the point(s) where two graphs meet.
- Practice Using our Calculators
- TI 83/84: Basic Skills
- CASIO fx: Basic Skills
- Practice 1 [Practice 1 Answer Key]
- Practice 2 [Practice 2 Answer Key][video for TI] [regression with casio]
Solve Problems
Problem Solving: putting it all together.
Skill Building:
Video/Calculator Summary:
Problem Review [Quiz 2019] Original and Answer Key
Extra Practice: Quadratic Problem Solving Review
Solve Problems
- Given the equation.
- Find the equation using 'regression' skills.
Problem Solving: putting it all together.
Skill Building:
- Part One and Part One Key
- Part Two and Part Two Key
- Part Three and Part Three Key
Video/Calculator Summary:
- Minimum and/or Maximum: [TI83/84] [Casio]
- X-Intercpets (zeros/roots) : [TI83/84] [Casio]
- Intersection {y2=) [TI83/84, 6:45 mark] [Casio]
- Quad Regression: [TI83/84] [Casio]
- Window [-10, 10, 1] [minimum, maximum, scale]
- TI 'zoom 6'
- Casio 'stnd'
Problem Review [Quiz 2019] Original and Answer Key
Extra Practice: Quadratic Problem Solving Review
Assessment Day:
Properties of Quadratics: factored format y=a(x-r)(x-s)
Lesson: (video summary)
- Quiz: Properties of Quadratics and Problem Solving
Properties of Quadratics: factored format y=a(x-r)(x-s)
- Find the x-intercepts using an algebraic method: create an equation where each factor equals zero and solve.
- Use symmetry of the x-intercepts to determine the equation for the axis of symmetry.
- Find the y value of the Vertex using the x value from the symmetry of the x-intercepts.
- Use the quadratic function to solve for the y-value algebraically.
- Use the graph to find the y-value: use trace or use the table function.
Lesson: (video summary)
Properties of Quadratics - vertex format y=a(x-h)^2+k
- When a quadratic function is written in this format, the vertex is the point V(h,k).
- The axis of symmetry passes through the vertex. The equation can be found by solving x-h=0, which is x=h.
- The value of 'a' in all our quadratics determines if the function opens up (positive 'a') or opens down (negative 'a').
Lesson:
Finding Equations
- Use the given information to determine which of the three equation formats you should use to solve the problem.
- Most of our problems involve finding the value of 'a' in the equation to determine the direction the function opens and the shape of the function.
- To check your answer, graph to see that the function has the properties required.
- We use a variety of skills from this chapter to algebraically solve problems.
Review: Quadratic Functions and problems
- Quiz (old exam): Properties of quad functions (vertex, symmetry, intercepts), problem solving (max, min, zeroes, intercept) and work with factored form and vertex form.
- 2017 Quiz1: Original and Answer Key