Upload
hannah-pearson
View
217
Download
0
Tags:
Embed Size (px)
Citation preview
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 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?
Practice - Worksheet
For your classwork today, I will be grading you on Mathematical Standard #2 – Reasoning Abstractly and Quantitatively.
Warm-Up, 9/101. 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?
What is “Standard Form”?
The standard form of a quadratic equation is written as:
f(x) = ax2 + bx + c
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.
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”.
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.