Identifying Key Features of Graphs of Quadratic Functions Algebra 2, Week 3 Standard 3: Identifying Key Features of Graphs of Quadratic Functions (Monday and Tuesday)

Warm-Up, 9/9 Quiz Feedback/Corrections Now that we have quizzed on two standards, what are some of the ways you think you can work to improve your score this week?

What can you say about this graph What can you say about this graph? What do you think are some of the “key points”?

What is a quadratic? A quadratic is an equation with one or more terms in which one of the terms is raised to a power of 2. The shape of a quadratic is called a parabola. THINK! How is the shape of a quadratic related to its definition?

Key Features of Quadratics Maximum Minimum Vertex Zeroes Y-Intercept Axis of Symmetry Domain Range

Examples: Name Key Characteristics

Work Together! Identify the key characteristics of the graphs below. 1. 2.

Practice - Worksheet For your classwork today, I will be grading you on Mathematical Standard #2 – Reasoning Abstractly and Quantitatively.

Warm-Up, 9/10 1. What is a quadratic? 2. What are the the key characteristics we can identify for quadratics? 3. Identify the key points of the graph:

Review of Key Characteristics What are the key characteristics of a quadratic? What do they tell us about a graph?

In your notebook, sketch a graph of the following... 1. The graph of a quadratic with a vertex of (0, -4) and zeroes at (-2, 0) and (2, 0). 2. What is the axis of symmetry for the graph you sketched for #1? How do you know?

3. Now sketch a graph with a y-intercept of (0, 6) and zeroes (-1, 0) and (1, 0). Check your work with a partner 4. What is the vertex here? How do you know?

Practice – Worksheet As you complete today's assignment, I will be grading you on the Mathematical Standard: Attending to Precision.

Warm-Up, 9/11 1. State the zeroes, y-intercept, axis of symmetry, vertex, domain, and range of the graph below: 2. Given an equation of a quadratic, such as f(x) = x2 +3x – 4, what are some ways you could try to graph it?

Standard 4: Graphing Quadratics from Standard Form (Wednesday and Thursday)

What is “Standard Form”? The standard form of a quadratic equation is written as: f(x) = ax2 + bx + c

What are the terms of a quadratic? Linear Constant What do they do to the graph?

Quadratic Term The term that is raised to the power of 2. Responsible for concavity (up or down) and the parabolic shape of a quadratic.

Linear Term The term with the variable raised to a power of 1. Responsible for shifting the graph horizontally.

Constant Term The term without a variable. How is the constant term related to the y- intercept?

How can we use standard form equations to graph quadratics? Find axis of symmetry: x = -b/2a Use substitution to find points on each side of the axis of symmetry. The axis of symmetry is always halfway between the x intercepts.

Using Substitution as a Strategy.. . Once you know the axis of symmetry, it is easy to find other points on the graph using substitution. Pick x values that are close to the axis of symmetry and evaluate the function using that x value. Set up a table of (x, f(x)) to help you keep track of your points!

Work Together Graph the following two equations in your notebooks: 1. f(x) = -x2 + 6x – 5 2. f(x) = 2x2 – 8x + 6

Practice While you are working on today's classwork, I will be grading you on the standard “attending to precision”.

Thursday, September 12 Practice Day!

Warm-Up, 9/12 Graph the following quadratics, and state the zeroes, vertex, axis of symmetry, and y- intercept. 1. f(x) = -x2 + 3x – 7 2. g(x) = 3x2 + x - 2

Practice While you are working on today's classwork, I will be grading you on problem-solving perseverance.

Friday, 9/13 QUIZ DAY!