Download 2.2B Graphing Quadratic Functions in Standard Form

2.2B Graphing Quadratic Functions in Standard Form
Objectives:
F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Paper/pencil graphing with standard form:
1. Does the parabola opens up or down?
2. Does it have a maximum or minimum?
3. What is the equation of the axis of symmetry? Graph the line.
4. What is the vertex. Plot the point.
5. What is the domain and range?
6. What is the y-intercept. Plot it.
7. Use the axis of symmetry to determine the point symmetric to the y-intercept. Plot it.
8. Graph the parabola.
Open the book to page 69 and 70 and read example 2.
Example: a. Consider the function f(x) = 2x2 – 4x + 5
1. a is positive: opens up
2. minimum
3. x = -(-4)/2(2) = 4/4 = 1
x=1
2
4. f(1) = 2(1) – 4(1) + 5 = 3 (1, 3)
5. domain: all real numbers
range: {y|y ≥ 3}
6. f(0) = 5, (0, 5)
7. (2, 5)
Example: b. Consider the function f(x) = -x2 – 2x + 3
1. a is negative: opens down
2. maximum
3. x = -(-2)/2(-1) = 2/-2 = -1 x = -1
4. f(-1) = -(-1)2 – 2(-1) + 3 = 4 (-1, 4)
5. domain: all real numbers
range: {y|y ≤ 4}
6. f(0) = 3, (0, 3)
7. (-2, 3)
Graphing Activity:
Practice: a. Consider the function f(x) = -x2 – 4x
1. a is negative, the graph opens down
2. maximum
3. x = -(-4)/2(-1) = 4/-2 = -2
4. f(-1) = -(-2)2 – 4(-2) = 4
(-2, 4)
5. domain: all real numbers
Range: {y|y ≤ 4}
6. (0, 0)
7. (-4, 0)
b. Consider the function f(x) = x2 + 3x – 1
1. a is positive, the graph opens up
2. minimum
3. x = -3/2(1) = -3/2
4. f(-3/2) = (-3/2)2 – 4(-3/2) – 1 = -13/4
(-3/2, -13/4}
5. domain: all real numbers
range: {y|y ≥ -13/4}
6. (0, -1)
7. (-3, -1)
Assessment:
Question student pairs.
Independent Practice:
Handout 2.2B
For a Grade:
Assignment 2.2B