1. 5-Minute Check APK F(x) = 5x+50 5(6) + 50 = $80.00
Find a linear function that describes the situation, and solve the problem.
1) A tractor rents for $50, plus $5 per engine hour. How much does it cost to rent and run the tractor for 6 hours?
F(x) = 5x+50
5(6) + 50 = $80.00

2. Quadratic Functions Objectives:
Students will be able to graph quadratic functions by finding the axis of symmetry & vertex..
Why? So you can apply these principles to real-world situations.
Mastery is 80% or better on 5 min checks and Indy work.

3. Concept Development- Graphs of Quadratic Functions
Using a graphing calculator, graph the equation y = x2.
What is the lowest point on the graph?
(0,0)
Which axis divides the graph in half?
y-axis
Using a graphing calculator, graph each of the following equations.
y = 2x2 y = 2x y = 2x2 – 4x

4. Quadratic Function
A function (f) defined by an equation of the form y = ax2 + bx + c, where a,b, and c are real numbers and a = 0, is a quadratic function and can be written f(x) = ax2 + bx + c.
The graph of a quadratic function is called a parabola.

5. Skill Dev-Example 1 Graph the quadratic function f(x) = -x2. x f(x) -2y
f(x) = -x2 x
f(x) -2 -1 1 2 -4 x -1 -1 -4

6. Skill Dev- Example 1 Graph the quadratic function f(x) = -x2. y
The vertex is the maximum or minimum point of a parabola.
vertex
If the graph of a parabola is folded so that the two sides of the parabola coincide, then the fold line is the axis of symmetry. x
axis of symmetry

7. Vertex and Axis of Symmetry
For a parabola defined by the equation
y = ax2 + bx + c:
the x-coordinate of the vertex is
2) the axis of symmetry is the line

8. Skill Dev- Example 2
Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x2 - 8x + 4 . y x
y-coordinate of vertex:
y = 2x2 – 8x + 4
= 2(2)2 – 8(2) + 4
= 8 –
= -4
vertex: (2,-4)

9. Guided-Example 2
Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x2 - 8x + 4 . y
axis of symmetry:
f(x) = 2x2 – 8x + 4 x
f(x) 1 2 3 4 x
x = 2 4 -2 -4 -2 4

10. Closing Exercise CFU
Find the vertex and axis of symmetry, then determine the number of solutions. Hint Quad Formula Last, graph the function.
1) f(x) = -2x2 + 4x + 1
Axis = 1
Vertex = 3
Maximum
2) g(x) = x2 -3x + 1
Axis = 1.5
Vertex = -1.25
Minimum

11. Students will be able to graph quadratic functions by finding the axis of symmetry & vertex..
Mastery is 80% or better on 5- Minute checks & Indy work.
What have you learned?

12. Homework
PDF Online