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