5-Minute Check APK 2 Solutions Discriminant= 64 X ints 1 and -3 Determine the number of solutions, Discriminant and find the roots if any (x-intercepts). Round to the nearest tenth   2 Solutions Discriminant= 64 X ints 1 and -3

Quadratic Functions Objectives: Students will be able to graph quadratic functions by finding the x intercepts (if any) or using test points (when there are no x intercepts), axis of symmetry & vertex Why? So you can apply these principles to real-world situations. Mastery is 80% or better on Indy work.

Concept Development- Graphs of Quadratic Functions Using a graphing calculator, Desmos or Discovery math tool, 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.

With a partner discuss the following: 1. What is the first step in solving the quadratic function using the quadratic equation? How can you determine the number of solutions? Why are the solutions important? Can you graph a quadratic function that has zero solutions (roots)?

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 1 Graph the quadratic function f(x) = -x2. y How can we find the axis of symmetry and vertex here? vertex x 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. axis of symmetry

Skill Dev-Example 1 Graph the quadratic function f(x) = -x2 Using test points. What is the axis of symmetry? What is the vertex f(x) = -x2 y x f(x) -2 -1 1 2 -4 x -1 -1 -4

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. Check DESMOS or Discovery to see if your graph is accurate. Axis = 1 Vertex = 3 Maximum 1) f(x) = -2x2 + 4x + 1 Axis = 1.5 Vertex = -1.25 Minimum 2) g(x) = x2 -3x + 1

Vertex (1,3) (-.225, 0) X-int (2.225, 0) X-int   Vertex (1,3) When you test 0 and 2 what do you get? (-.225, 0) X-int (2.225, 0) X-int

When you plug in 3 and 0 as test points what do you get? X-int (.382, 0) X-int (2.618,0) Vertex (1.5, -1.25)

What have you learned? Students will be able to graph quadratic functions by finding the x intercepts (if any) or using test points (when there are no x intercepts), axis of symmetry & vertex Why? So you can apply these principles to real- world situations. Mastery is 80% or better on Indy work.

Homework PDF Online Axis of Symm & Vertex