5.1 - Vertex Form of Quadratic Functions Part 1&2 Lesson 1

Graphs of Quadratic Functions in Vertex Form 𝑦 𝑎 𝑥 𝑝 𝑞

𝒚 𝒙𝟐 Part I: ____________________ 𝑎 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 Vertex ( , ) Graph 𝑦 𝑥 𝑎𝑛𝑑 𝑦 𝑥 using a table of values. The sign of a (the coefficient of x2)determines .

If the parabola opens UPWARD:

o The vertex is the point on the graph and the y‐value of the

vertex is the value.

If the parabola opens DOWNWARD:

o The vertex is the point on the graph and the y‐value of the vertex is

the value.

The parabola is symmetric about a line called .

o The axis of symmetry intersects the vertex and the x‐value of the vertex is the

equation of the axis of symmetry .

Graphs of Quadratic Functions in Vertex Form 𝑦 𝑎 𝑥 𝑝 𝑞

𝒚 𝒙𝟐 𝒒 Part II: ____________________ 𝑎 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 Vertex ( , )

𝑦 𝑥 2 Coordinate of vertex: ( , ) 𝑦 𝑥 1 Coordinates of vertex: ( , ) The q shifts Describe what is happening to the parabola in each situation?

a) 𝑦 𝑥 4

b) 𝑦 𝑥

c) 𝑦 𝑥

d) 𝑦 𝑥 1

5.1 - Vertex Form of Quadratic Functions Part 3&4 Lesson 2

Graphs of Quadratic Functions in Vertex Form 𝑦 𝑎 𝑥 𝑝 𝑞

𝒚 𝒙 𝒑 𝟐 Part III: ____________________ 𝑎 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 Vertex ( , )

𝑦 𝑥 2 𝑦 𝑥 𝑝 Take *note* the shift horizontally is the OPPOSITE sign of what is in the bracket. This is because the negativesign inside the equation Coordinate of vertex: ( , ) 𝑦 𝑥 3 Coordinates of vertex: ( , ) The pshifts the parabola .

𝑦 𝑥 𝒑 𝒒 Graph: 𝑦 𝑥 2 3 Vertex ( , ) Graph: 𝑦 𝑥 5 2 Vertex ( , )

Graphs of Quadratic Functions in Vertex Form 𝑦 𝑎 𝑥 𝑝 𝑞

𝒚 𝒂𝒙𝟐 Part IV: ____________________ 𝑎 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 Vertex ( , )

1 𝑦 2𝑥

2 𝑦14

𝑥

If a is bigger than 1 If ais between 0 and 1 Describe what is happening to the parabola in each situation?

a) 𝑦 𝑥 4

b) 𝑦 𝑥 3 2

c) 𝑦 3 𝑥 7

d) 𝑦 𝑥 1

e) 𝑦 𝑥 3

5.1 - Vertex Form of Quadratic Functions Lesson 3

𝑦 𝑎 𝑥 𝑝 𝑞

Characteristics of a Quadratic Function - Parabola

Coordinates of the vertex

Axis of Symmetry

Stretch Factor

Direction of Opening

Max/Min Value

Domain

Range

Ex#1: Determine the quadratic function from the following graph. Ex#2: Determine the quadratic function from the following graph.

Ex#3: Determine the quadratic function with a vertex (2,-3) and passes through point (0,5). Ex#4: Determine the quadratic function with a y-intercept of 1 and vertex (2,3). Ex#5: The goalkeeper kicked the soccer ball from the ground. It reached a maximum height of 24.2 m after 2.2 s. The ball was in the air for 4.4 s.

a) Define the quadratic function to represent the height of the ball above the ground. b) How high was the ball after 4 s?

5.2 - Intercepts / Domain and Range

Graphs of Quadratic Functions in Vertex Form: 𝑦 𝑎 𝑥 𝑝 𝑞

Recall: What is an intercept? What is a graphs domain/range? What is the parabolas maximum/minimum value?

The Nature of the Roots are the number of or times the graph crosses the . You can determine the nature of the roots with a quick sketch:

Determine/plot the vertex Determine the direction of opening

a) 2( ) 0.5 7f x x b)

2( ) 2( 1)g x x c) 21

( ) ( 5) 116

f x x

How do you find the y-intercept? Let = 0 1. Graph: 𝑦 𝑥 2 4

𝑝 𝑞 𝑎 Coordinates of vertex: Axis of symmetry: Opening: Range: Domain: How many x-intercepts: y-intercept:

2. Graph: 𝑓 𝑥 𝑥 4 2 𝑝 𝑞 𝑎

Coordinates of vertex: Axis of symmetry: Opening: Range: Domain: How many x-intercepts: y-intercept: 3. Determine the equation of the graph.

𝑝 𝑞 𝑎

SummarizeCoordinates of vertex: Equation of axis of symmetry: Opening: Range: Domain: How many x-intercepts: y-intercept: