𝒚= 𝟐𝒙 𝟐 +𝒙+𝟑 Warm-Up 1.) If x=-1, find the y-value. 2.) Write your x and y value as a coordinate point. 3.) How do we find the axis of symmetry? 4.) What is your axis of symmetry?

9.1 Day 2 Graphing Quadratics in standard form Day 2 Algebra 1

Objectives I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator

How do I graph in Standard Form? 𝒚=𝒂 𝒙 𝟐 +𝒃𝒙+𝒄 1. Find the x-coordinate of the vertex: x=− 𝑏 2𝑎 (This is axis of symmetry – a.o.s.) 2. Draw and fill out a table of values. Begin with the a.o.s. for ‘x’ value! Shortcut - Find the y-intercept and plug in that ordered pair! 3. Plot 5 points and draw a smooth curve to connect them! ***USE ARROWS*** x a.o.s. y

Example 1: Graph 𝑦= −2𝑥 2 +4𝑥+1 Vertex: _________   y-intercept: _________ axis of symmetry: _________ Domain: _________ Range: ________ What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

What Can I find From My Graph? Equation for Axis of Symmetry In y = 2 𝑥 2 + 4x + 1, a = 2 and b = 4. Substitute these values into the equation of the axis of symmetry. x = – 𝑏 2𝑎 x = – 4 2(2) = –1 The axis of symmetry is x = –1. Coordinates of the Vertex Since the equation of the axis of symmetry is x = –1 and the vertex lies on the axis, the x–coordinate of the vertex is –1. y = 2 𝑥 2 + 4x + 1 Original equation y = 2 (−1) 2 + 4(–1) + 1 Substitute. y = 2(1) – 4 + 1 Simplify. y = –1 The vertex is at (–1, –1). Y-Intercept: The point where the parabola crosses the ‘y’ axis. This can be found by substituting a 0 in for ‘x’. Minimum: If lead coefficient is + (Parabola Opens Upward) then vertex is at BOTTOM. This is a minimum! Maximum: If lead coefficient is - (Parabola Opens Downward) then vertex is at TOP. This is a maximum! Domain: All ‘x’ Values Range: All ‘y’ Values Number of Solutions: This is based on # of time the Parabola CROSSES the ‘x’ axis

Practice 2: Graph 𝑦= 3𝑥 2 +12𝑥+3 Vertex: _________   y-intercept: _________ axis of symmetry: _________ Domain: _________ Range: ________ What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

Practice 3: Graph 𝑦= −𝑥 2 −4𝑥−8 Vertex: _________   y-intercept: _________ axis of symmetry: _________ Domain: _________ Range: ________ What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

Practice 4: Graph 𝑦= −2𝑥 2 −8𝑥+1 Vertex: _________   y-intercept: _________ axis of symmetry: _________ Domain: _________ Range: ________ What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

End of Day 2 Homework: 9.1 Standard Form Practice Worksheet Announcements: - Tomorrow we will graph with vertex form!

9.1: Graphing Quadratics in vertex form Day 3 Algebra 1

Warm up x y   Graph 𝒚=𝟒 𝒙 𝟐 −𝟒𝒙+𝟏 Vertex: _________ y-intercept: _________ axis of symmetry: _________ Domain: _________ Range: ________

Objectives I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator

How do I graph in Vertex Form? 𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌 1. Find the vertex. Since the equation is in vertex form, the vertex will be at the point 𝒉, 𝒌 * CHANGE ON YOUR NOTES ** Some people might like to think of this as opposite of h which is fine, but please note that h must be subtracted from x to be in true vertex form 2. Draw and fill out a table of values. Begin with the a.o.s. for ‘x’ value! Shortcut - Find the y-intercept and plug in that ordered pair! 3. Plot 5 points and draw a smooth curve to connect them! ***USE ARROWS*** x y

Example 1: Graph 𝑦= −2(𝑥+1) 2 +2 y   (a.o.s) Vertex: _________   y-intercept: _________ axis of symmetry: _______ Domain: _________ Range: ________ What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

Practice 1: Graph 𝑦= 3(𝑥−2) 2 −4 What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

Practice 2: Graph 𝑦= −(𝑥+5) 2 −2 What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

Practice 3: Graph 𝑦= (𝑥−3) 2 +1 What is the vertex? What is the equation for the axis of symmetry? Is the vertex a maximum or a minimum? What are the Domain and Range? How many solutions does the equation produce?

END OF DAY 3 Homework: Vertex Form Practice Worksheet Announcements: Tomorrow we will learn intercept form!

9.1: Graphing Quadratics in intercept form Day 4 Algebra 1

Warm up Graph 𝑓 𝑥 = (𝑥+3) 2 +4 Vertex: _________ y   (a.o.s) Vertex: _________   y-intercept: _________ axis of symmetry: _______ Domain: _________ Range: ________

Objectives I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator

How do I graph in Intercept Form? 𝒚=𝒂(𝒙−𝒑)(𝒙−𝒒) Identify intercepts: 𝒑,𝟎 & (𝒒,𝟎) Find the x-coordinate of the vertex: 𝐱= 𝒑+𝒒 𝟐 Find the y-coordinate: Plug in x. Graph the line of symmetry: x = # Plot 2 more points and draw curve

Example 1: Graph 𝑦=(𝑥−2)(𝑥+4)

Practice 1: Graph 𝑦=−(𝑥−3)(𝑥+2)

Practice 2: Graph 𝑦=(𝑥−1)(𝑥+3)

Practice 3: Graph 𝑦=−(𝑥+3)(𝑥+5)

End of day 4 Homework: Intercept Form practice worksheet Announcements: New calendar! Retake forms complete! Schedule retake!