Class Greeting. Chapter 10 Quadratic Equations and Functions Lesson 10-4 Graphing Quadratic Equations.

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Presentation transcript:

Class Greeting

Chapter 10 Quadratic Equations and Functions Lesson 10-4 Graphing Quadratic Equations

Objective: The students will be able to graph quadratic equations.

The graph of every quadratic equation has exactly one y-intercept. The number of x-intercepts, however, can vary. Guidelines for Sketching a Parabola

a function of the form y = ax 2 + bx + c where a ≠ 0 the graph of a quadratic function

Vocabulary when something has sides that are mirror images of each other. The thing is said to be symmetrical. Do Not Copy

for y = ax 2 + bx + c the axis of symmetry is Parabolas are Symmetrical about the axis of symmetry.

Example 1-3a Consider the graph of Write the equation of the axis of symmetry. In Equation for the axis of symmetry of a parabola and Answer: The equation of the axis of symmetry is y = ax 2 + bx + c

the minimum or maximum point of the parabola.

How to find the vertex: 1.Find the Axis of Symmetry 2.Then put that value of x into your quadratic equation and solve for y.

Example 1-3b Consider the graph of Find the coordinates of the vertex. Since the equation of the axis of symmetry is x = –2 and the vertex lies on the axis of symmetry, the x -coordinate for the vertex is –2. Answer: The vertex is at (–2, 6). x = –2 (from example 1)

How to graph a Quadratic Function. 1.Find the Axis of Symmetry. 2.Then put that value of x into your quadratic equation to find the vertex. 3.Make a table to find 4 more points. 4.Graph the parabola.

Example 1-3f (–2, 6) (–1, 4)(–3, 4) (0, –2) (–4, –2) Graph the function:Equation for the axis of symmetry Find the coordinates of the vertex. The vertex is at (–2, 6). x –1 y 4 Find 4 more points. x –1–3 y 44 x –1–3 0 y 44–2–2 x –1–3 0–4 y 44–2–2–2

Example 1-3g Consider the graph of a. Write the equation of the axis of symmetry. b.Find the coordinates of the vertex. Answer: (1, –2) Answer: c.Graph the function.

Example 1-3h d.Graph the function. Answer: Consider the graph of

Real World Word Problem

Lesson Summary: Objective: The students will be able to graph quadratic equations.

Preview of the next Lesson: Objective: The students will be able to define a relation; identify the domain and range of a relation; represent relations as tables, graphs, and mappings; determine if relations are functions; and evaluate functions for given values.

Homework / 5-39 odd

Stand Up Please