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9.1 Exploring Quadratic Graphs. Objective: SWBAT graph quadratic functions and find roots or x -intercepts. Mini Quiz 22. 2. Overview. Quadratic functions y = ax 2 + bx + c (no b for today) Identifying maximum and minimum Comparing widths of parabolas Graphing the parabola

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9 1 exploring quadratic graphs

9.1 Exploring Quadratic Graphs

Objective: SWBAT graph quadratic functions and find roots or x-intercepts.

overview
Overview

Quadratic functions y = ax2 + bx + c (no b for today)

  • Identifying maximum and minimum
  • Comparing widths of parabolas
  • Graphing the parabola
  • Finding the vertex
quadratic function
Quadratic Function

Standard Form:

Parabola: U-shaped graph for quadratic function

What is a, b, and c for the following quadratic functions?

1. y = 2x2 + 3x – 4

2. y = x2 – x + 9

3. y = -x2 – 7

Leading Coefficient

Vertex-

highest or lowest point on the parabola

parabola quadratic functions
Parabola – Quadratic Functions

Important “Points”

x-intercepts, roots, zeros

Does the graph have a maximum or a minimum?

vertex (on the axis of symmetry x = #)

vertex axis of symmetry and max or min
Vertex, Axis of Symmetry, andMax or Min

1.

Vertex (0, 0); x = 0; Min

2.

Vertex (-2, 4); x = -2; Max

3.

Vertex (4, 3); x = 4; Max

4.

Vertex (1, -2); x= 1; Min

Identify the vertex and axis of symmetry. Tell whether it is a minimum or maximum.

who s the widest of them all
Who’s the widest of them all?

Widest:

The “smaller” the “a” is, the wider the graph

graphing the parabola
Graphing the Parabola

Steps:

1. Make a T-chart

2. Find the vertex:

(axis of

symmetry)

3. Graph 2 points to each side of the vertex

4. Draw the parabola

5. Write the x-intercepts

x = -2, x = 0

Graph: y = x2 + 2x

1

3

0

0

-1

-1

-2

0

-3

3

graph and write the x intercepts
Graph and Write the x-intercepts

x = 0

x = 0

x = No

Solution

x = -2

x = 2

wrap up
Wrap Up

Quadratic functions y = ax2 + bx + c (no b for today)

  • Identifying maximum and minimum
  • Comparing widths of parabolas
  • Graphing the parabola
    • Find vertex:
    • Pick 2 points on each side of the vertex
    • Graph the parabola

HW: P. 429 #1-29 EOO

DLUQ: What is the formula for the axis of symmetry and the vertex for the x-coordinate?