WARM-UP: DISCUSS WITH YOUR PARTNER

1

Consider the function y = 3x2 – 6x + 2.

a) Does the graph open up or down?

b) Find the line of symmetry of the graph of the function.

c) Find the vertex of the graph of the function.

d) Find the y-intercept.

Opens Up

x = 1

(1, -1)

y = 2

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Graphing Quadratic FunctionsAlgebra Unit 11

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STEPSTo graph a quadratic function perform the following steps:

STEP 1: Put equation in standard form y = ax2 + bx + c.

STEP 2: Find the line of symmetry using and graph it.

STEP 3: Find the vertex and plot it.

STEP 4: Find two other points using a table.• Use the next two numbers after the line of symmetry for the

table.

• Reflect points across the line of symmetry.

• Connect the five points with a smooth curve.

a

bx

2

ya

b,

2

4

STEP 1: Put equation in standard form y = ax2 + bx + c.

STEP 2: Find the line of symmetry and graph it.

MODELINGGraph y = 2x2 – 4x – 1.

Already in standard form.

y

x

Thus the line of symmetry is x = 1.

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STEP 3: Find the vertex and plot it.

MODELINGGraph y = 2x2 – 4x – 1.

y

x

Plug in x = 1 to find the y – value of the vertex.

Thus the vertex is (1 ,–3).

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STEP 4: Find two other points using a table.

MODELINGGraph y = 2x2 – 4x – 1.

y

x

(1 ,–3)

3

2

yx

–1

5

Reflect points across the line of symmetry.

Use the next two numbers after the line of symmetry for the table.

Connect the five points with a smooth curve.

(2 ,–1)

(3 ,5)

(0,–1)

(–1,5)

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y

x

STEP 1: Put equation in standard form y = ax2 + bx + c.

STEP 2: Find the line of symmetry and graph it.

Graph y = – 2x2 – 8x + 1.

Already in standard form.

Thus the line of symmetry is x = – 2.

STRUCTURED PRACTICE

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STEP 3: Find the vertex and plot it.Graph y = – 2x2 – 8x + 1.

y

x

Plug in x = – 2 to find the y – value of the vertex.

Thus the vertex is (–2, 9).

STRUCTURED PRACTICE

9

y

x

STEP 4: Find two other points using a table.

Graph y = – 2x2 – 8x + 1.

(–4,1)

0

–1

yx

7

1

Reflect points across the line of symmetry.

Use the next two numbers after the line of symmetry for the table.

Connect the five points with a smooth curve.

(–3,7) (–1 ,7)

(0,1)

(–2,9)

STRUCTURED PRACTICE

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INDEPENDENT PRACTICE

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