Warm up!
1. 𝑦 = −6𝑥 + 2
When x=3, what does y=?
2. 𝑦 = 𝑥 2 − 2𝑥 + 5
When x=5, what does y=?
3. 𝑦 = 3𝑥 − 7
When y=11, what does x=?
Day 33 Topic
Quadratics
Objective
The student will be able to graph a quadratic equation.
Equations and Graphs:
Linear Equation
𝑦 = 𝑚𝑥 + 𝑏
Shape:
Quadratic Equation
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
Shape:
A _________________________ is one in which the largest exponent is _______.
It looks like a __________ and is described by an equation of the following form:
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
If 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 identify a, b, and c for each quadratic function.
1. 𝑦 = 𝑥 2 + 4𝑥 + 4
4. 𝑦 = −3𝑥 2 + 12𝑥 − 6
a=_____, b=______, c=______
a=_____, b=______, c=______
2. 𝑦 = 𝑥 2 − 6𝑥 + 7
5. 𝑦 = 2𝑥 2 − 8
a=_____, b=______, c=______
a=_____, b=______, c=______
3. 𝑦 = 3𝑥 2 + 8𝑥 − 9
6. 𝑦 = 6𝑥 − 3𝑥 2
a=_____, b=______, c=______
a=_____, b=______, c=______
Ex. 1
Graph y=x2. Identify the vertex
General Information about Quadratics
Parabola
Axis of Symmetry
Vertex
Ex. 2
Graphing Quadratic Functions
METHOD 1:
Standard Form
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
METHOD 2:
Vertex Form
𝑦 =𝑎 𝑥−ℎ
METHOD 3:
Intercept Form
𝑦 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
2
+𝑘
METHOD 1:
1.
Standard Form 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
𝑦 = −𝑥 2 + 2𝑥 + 3
Step 1: a=______, b=______, c=______
Step 2: opens up or down?
Step 3: Find one coordinate point.
Step 4: Find the x-coordinate of the vertex:
−𝑏
𝑥=
2𝑎
Step 5: Find the y-coordinate of the vertex
(Plug in x-coord. from above)
Step 6: Find the axis of symmetry
YOU TRY
2.
METHOD 1:
1
𝑦 = 2 𝑥 2 + 2𝑥 − 1
Step 1: a=______, b=______, c=______
Step 2: opens up or down?
Step 3: Find one coordinate point.
Step 4: Find the x-coordinate of the vertex:
−𝑏
𝑥=
2𝑎
Step 5: Find the y-coordinate of the vertex
(Plug in x-coord. from above)
Step 6: Find the axis of symmetry
Standard Form 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
METHOD 2:
3.
𝑦 =2 𝑥−1
2
−3
Step 1: opens up or down?
Step 2: Find one coordinate point.
Step 3: Find the vertex.
Step 4: Find the axis of symmetry.
Vertex Form
𝑦 =𝑎 𝑥−ℎ
2
+𝑘
YOU TRY
4.
𝑦 =− 𝑥+5
METHOD 2:
2
+2
Step 1: opens up or down?
Step 2: Find one coordinate point.
Step 3: Find the vertex.
Step 4: Find the axis of symmetry.
Vertex Form
𝑦 =𝑎 𝑥−ℎ
2
+𝑘
METHOD 3:
5.
Intercept Form
𝑦 = 2(𝑥 − 3)(𝑥 − 1)
Step 1: opens up or down?
Step 2: Plot the intercepts.
Step 3: Find the axis of symmetry.
Step 4: Find the vertex.
𝑦 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
YOU TRY
6.
METHOD 3:
𝑦 = −(𝑥 + 2)(𝑥 − 3)
Step 1: opens up or down?
Step 2: Plot the intercepts.
Step 3: Find the axis of symmetry.
Step 4: Find the vertex.
Intercept Form
𝑦 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
A. Opens up or down
B. Vertex coordinates, max or min
C. Axis of symmetry
D. Sketch the graph