1. 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?

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

3. 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?

4. 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

5. 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?

6. What Can I find From My Graph?
Equation for Axis of Symmetry
In y = 2 𝑥 x + 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 x Original equation
y = 2 (−1) (–1) + 1 Substitute.
y = 2(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

7. 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?

8. 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?

9. 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?

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

11. 9.1: Graphing Quadratics in vertex form Day 3
Algebra 1

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

13. 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?

14. 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

15. Example 1: Graph 𝑦= −2(𝑥+1) 2 +2y
(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?

16. 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?

17. 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?

18. 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?

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

20. 9.1: Graphing Quadratics in intercept form Day 4
Algebra 1

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

22. 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?

23. 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

24. Example 1: Graph 𝑦=(𝑥−2)(𝑥+4)

25. Practice 1: Graph 𝑦=−(𝑥−3)(𝑥+2)

26. Practice 2: Graph 𝑦=(𝑥−1)(𝑥+3)

27. Practice 3: Graph 𝑦=−(𝑥+3)(𝑥+5)

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