1. 4.1 Notes – Graph Quadratic Functions in Standard Form

2. Parabola that is a function in the shape of a U
Quadratic Function
Standard Form
Vertex
Axis of Symmetry
Parabola that is a function in the shape of a U
y = ax2 + bx + c
Max or Min of a parabola
Line that splits the graph vertically

3. Transformations of a, b, and c.
y = ax2 + bx + c
Positive #
Negative # a
Opens up
Opens down
Has minimum
Has maximum
a = 1, normal
a = –1, normal
Fraction, wide
Fraction, wide
a > 1, skinny
a < –1, skinny

4. Set y = 0, factor the equation and solve for x
x – intercepts
Set y = 0, factor the equation and solve for x
Two answers
One answer
No Real answers

5. Shift vertex left or right
y = ax2 + bx + c b
Shift vertex left or right c
y – intercept

6. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. This is the parent function.

7. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y) 2
(2, 4) 1
(1,1)
(0,0) –1
(–1,1) –2
(–2, 4)

8. (0,0) x = 0 y = 0 Vertex: ________________ axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = 0

9. (0,0)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = 0
(2, 4)
(1,1)
(0,0)
(–1,1)
(–2, 4)

10. 1. Put the equation in standard from
1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide.
Standard Form:
Opens up
wide

11. 1. Put the equation in standard from
1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide.
Standard Form:
Opens down
skinny

12. 1. Put the equation in standard from
1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide.
Standard Form:
Opens down
normal

13. 2. Identify the vertex. State the max or min.
(2, –13)
Vertex: ________________
min/max value: _________
y = –13

14. 2. Identify the vertex. State the max or min.
(1, 11)
Vertex: ________________
min/max value: _________
y = 11

15. 2. Identify the vertex. State the max or min.
(0, 5)
Vertex: ________________
min/max value: _________
y = 5

16. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

17. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y) 2
(2, 5) 1
(1, 8)
(0, 9) –1
(–1, 8) –2
(–2, 5)

18. (0, 9) x = 0 y = 9 3 x + 3 = 0 or x - 3 = 0 9 x = -3 x = 3
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = 9 3
x + 3 = 0 or
x - 3 = 0 9
x = -3
x = 3

19. (0, 9)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = 9 3 9
(2, 5)
(1, 8)
(0, 9)
(–1, 8)
(–2, 5)

20. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

21. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y) 4
(4, 6) 2
(2, 0)
(0, –2) –2
(–2, 0) –4
(–4, 6)

22. (0, –2) x = 0 y = –2  2 –2 Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = –2
 2 –2

23. (0, –2) x = 0 y = –2  2 –2 (4, 6) (2, 0) (0, –2) (–2, 0) (–4, 6)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 0
y = –2
 2 –2
(4, 6)
(2, 0)
(0, –2)
(–2, 0)
(–4, 6)

24. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

25. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y) 1
(1, –9)
(0, 0)
(–1, 3) –1 –2
(–2, 0) –3
(–3, –9)

26. (–1, 3) x = –1 -3x -3x -3x(x + 2) = 0 y = 3 -3x = 0 or x + 2 = 0 0, -2
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = –1
-3x x
-3x(x + 2) = 0
y = 3
-3x = 0 or
x + 2 = 0
0, -2
x = 0
x = -2

27. (–1, 3) x = –1 y = 3 0, -2 (1, –9) (0, 0) (–1, 3) (–2, 0) (–3, –9)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = –1
y = 3
0, -2
(1, –9)
(0, 0)
(–1, 3)
(–2, 0)
(–3, –9)

28. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

29. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y)
(0, 3) –1
(–1, 0)
(–2, –1) –2 –3
(–3, 0) –4
(–4, 3)

30. (–2, –1) x = -2 x 3 x 1 y = –1 3x + x -1, -3 (x + 3)(x + 1) = 0 3
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2 x 3 x 1
y = –1 3x + x
-1, -3
(x + 3)(x + 1) = 0 3
x + 3 = 0 or
x + 1 = 0
x = –3
x = –1

31. (–2, –1) x = -2 y = –1 -1, -3 3 (0, 3) (–1, 0) (–2, –1) (–3, 0)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
y = –1
-1, -3 3
(0, 3)
(–1, 0)
(–2, –1)
(–3, 0)
(–4, 3)

32. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

33. 3. Sketch the graph of the quadratic equations
3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. x
(x,y) 3
(3, –8) 2
(2, –2)
(1, 0) 1
(0, –2) –1
(–1, –8)

34. (1, 0) -2 -2 -2 x = 1 y = 0 1 -2 -2(x2 – 2x + 1) = 0 x -1 x -1 -x + -x
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 1
-2(x2 – 2x + 1) = 0 x -1
y = 0 x -1 1 -x + -x
-2(x – 1)2 = 0 -2
(x – 1)2 = 0
x – 1 = 0
x = 1

35. (1, 0) x = 1 y = 0 1 -2 (3, –8) (2, –2) (1, 0) (0, –2) (–1, –8)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 1
y = 0 1 -2
(3, –8)
(2, –2)
(1, 0)
(0, –2)
(–1, –8)