4.a  Graph Quadratic Functions [4.1, 4.2].notebook

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March 10, 2014

Oct 6­9:44 PM

Warm-up• Graph the following equations by finishing the

table.

Oct 6­9:44 PM

4.a Graph Quadratic Equations [4.1,4.2]

After this lesson you will be able to…

• Use a quadratic equation to find the vertex, axis of symmetry, direction of opening, and dilation and shape.

• Translate an equation in standard form to vertex form.

• Write an equation in vertex form from a given graph of a quadratic

Oct 6­9:44 PM

A quadratic function is a function described by an equation that can be written in the form

f(x)= ax2 + bx + c

A quadratic term is the term ax2 in the quadratic function

A linear term is the term bx in the quadratic function

A constant term is the term c in the quadratic function

Quadratic Functions

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Quadratic Functions and Their Graphs

• When graphed, quadratic functions create a parabola.

• A parabola is a U shaped graph.

• A parabola looks like

• The parent graph of a parabola is y=x2

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Let’s explore• Graph y=x2

• Let’s try adding and subtracting numbers…

• What do you notice?

> If we add a number, the graph shifts _____.

> If we subtract a number, the graph shifts ________

• Let’s try adding and subtracting numbers inside the square (y= (x ± #)2)…

• What do you notice?

> If we add a number, the graph moves to the _______

> If we subtract a number, the graph moves to the ________

• What happens if we make the x2 negative?> The graph _______ upside down

Oct 6­9:44 PM

BIG IDEA!!!Graph of any parabola can be written in the form

y = a(x - h)2 + k

• if h>0, the graph moves right |h| units

• If h<0, the graph moves to the left |h| units

• If k>0, the graph moves up |k| units

• If k<0, the graph moves down |k| units

4.a  Graph Quadratic Functions [4.1, 4.2].notebook

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March 10, 2014

Oct 6­9:44 PM

What do all these letters mean???

• Y is the y-coordinate

• A is the coefficient which dilates the graphs

> makes it wider or thinner

• X is the x-coordinate

• H is the number that shifts the graph right or left

> does not change the shape of the graph

• K is the number that shifts the graph up or down

> Does not change the shape of the graph

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Characteristics about the Graph

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Example 1:

• Use the equation to find the (1)vertex, (2) axis of symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range(. Then Graph!

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Example 2:• Use the equation to find the (1)vertex, (2) axis of

symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!

Oct 6­9:44 PM

Example 3:• Use the equation to find the (1)vertex, (2) axis of

symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!

Oct 6­9:44 PM

Example 4:• Use the equation to find the (1)vertex, (2) axis of

symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!

4.a  Graph Quadratic Functions [4.1, 4.2].notebook

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March 10, 2014

Oct 6­9:44 PM

Practice• Find the vertex, axis of symmetry, direction of opening,

dilation, domain and range of the following. Then graph!

Oct 6­9:49 PM

Oct 6­9:44 PM

Another way to find the Vertex …

• When the equation is NOT given to you in the form y = a(x - h)2 + k, it will be in this form..

y = ax2 + bx + c

• Use this to find the vertex….

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Let’s Practice

• Find the vertex of the following equations.

5) y = x2 + 8x + 71

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Let’s Practice

• Find the vertex of the following equations.

6) y = 3x2 – 6x – 5

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You Try…

• Find the vertex of the following equations.

7) y = x2 + 16x + 71

HINT use the equation

4.a  Graph Quadratic Functions [4.1, 4.2].notebook

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March 10, 2014

Oct 6­9:44 PM

You Try…

• Find the vertex of the following equations.

8) y = x2 – 2x – 5

HINT use the equation

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Example 9• Create the equation in vertex form which would graph the

given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.

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Example 10• Create the equation in vertex form which would graph the

given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.

Oct 6­9:44 PM

Example 11• Create the equation in vertex form which would graph

the given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.

Oct 6­9:44 PM

Example 12• Create the equation in vertex form which would graph the

given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.

Oct 6­9:44 PM

Example 13• Create the equation in vertex form which would graph the

given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.

4.a  Graph Quadratic Functions [4.1, 4.2].notebook

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March 10, 2014

Oct 6­9:44 PM

Homework:• ST 4.a both sides

• Checkpoint Tomorrow!

• Chapter 4 Test will be Tuesday 3/18!

Oct 6­9:47 PM