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

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.

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 = 2x2 + 1 y = 2x2 – 4x

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.

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

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

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

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 – 16 + 4 = -4 vertex: (2,-4)

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

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

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?

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