Homework Log

Fri

12/11

Lesson 4 – 1

Learning Objective: To graph quadratic functions

Hw: Graphing Parabolas Day 1 WS

12/11/15 Graphing Parabolas Day 1

Algebra II

To graph quadratic functions To determine the vertex & axis of symmetry of a parabola

To determine extreme values & whether it’s a max or min of a parabola

To determine x & y – intercepts of a parabola

Learning Objectives

Quadratic Function – Standard Form

Graph is a parabolaTo find Vertex, start with

Plug x into to find y of vertex

Axis of Symmetry – divides graph of parabola in half evenlyAxis of Symmetry is

Extreme Value – y-value of vertex

Quadratic Function – Vertex Form

Graph is a parabola

Vertex : (h, k)

Axis of Symmetry : x = h

Extreme Value – y-value of vertex

If a > 0 (positive) Opens up Has a minimum

If a < 0 (negative) Opens down Has a maximum

For all forms of quadratic functions

If < 1 Parabola is Compress It’s “Wide”

If > 1 Parabola is Stretched It’s “Narrow”

Intercepts & Solutions

x – intercept – a.k.a. root, zero, solution

Where graph crosses the x - axis

Plug in y = 0 & solve for x

May have to factor or quadratic formula!

y – intercept – plug in x = 0 & solve for y

Where graph crosses the y - axis

Parent Function

a = 1 Opens upVertex: x = 0 y = 0Vertex: (0, 0)AoS: x = 0MinMin/Extreme Value of 0

𝑓 (𝑥 )=𝑥2

Domain: All Real #sRange: y 0

x y

–2

–1

4

1

1

2

1

4

V( 0 0)

1.

a = –2 Opens downVertex: (– 1, 2)AoS: x = –1MaxMax/Extreme Value of 2

x – int: (y = 0) x = 0, -2x – intercept:(0, 0) & (-2, 0)

y-int: (x = 0) y = 0

y-int: (0, 0)

1.

Domain: All Real #sRange: y 2

x y

–3

–2

–6

0

0

1

0

–6

V(–1 2)

2.

a = 2 Opens upVertex: (– 3, 0)AoS: x = –3MinMin/Extreme Value of 0

root: (y = 0) x – intercept:(-3, 0)

y-int: (x = 0) y = 18

y-int: (0, 18)

2.

Domain: All Real #sRange: y 0

x y

–5

–4

8

2

-2

-1

2

8

V(–3 0)

3. a = 1 Opens upVertex: x = -3 y = 1V(-3, 1)AoS: x = -3

MinExtreme Value 1x – int: (y = 0) x – intercept:

y-int: (x = 0)

y-int: (0, 10)

3.

Domain: All Real #sRange: y 1

x y

–5

–4

5

2

-2

-1

2

5

V(–3 1)

4. a = -2 Opens downVertex: x = 0 y = 5V(0, 5)AoS: x = 0

MaxExtreme Value 5x – int: (y = 0) x – intercept:

y-int: (x = 0)

y-int: (0, 5)

4.

Domain: All Real #sRange: y 5

x y

–2

–1

-3

3

1

2

3

-3

V( 0 5)

Find Vertex & Axis of Symmetry5. Vertex: x = 4 y = 1V(4, 1)AoS: x = 4

Find Vertex & Axis of Symmetry6. Vertex: x = -6 y = -5V(-6, -5)AoS: x = -5

7.

a = Opens downVertex: (4, 3)AoS: x = 4MaxMax/Extreme Value of 3

7.

x – int: (y = 0) 0 x – intercept:(, 0)

y-int: (x = 0) y = – 5y-int: (0, -5)

7.

Domain: All Real #sRange: y 3

x y

2

3

1

2.5

5

6

2.5

1

V(4 3)

Graph What is the vertex? What is the axis of symmetry? What is the extreme value? Does it open up or down? Does it have a max or min? What are the x & y intercepts?

Ticket Out the Door

Assignment:

Graphing Parabolas Day 1 WS