Introduction to Quadratics

Transcription

1 Name: Date: Block: Introduction to Quadratics An quadratic function (parabola) can be expressed in two different forms. Vertex form: Standard form: a( x h) k ax bx c In this activit, ou will see how these forms are related to the graph, vertex location, width, and direction of the curve. Quadratic functions come in two basic forms: ones that point up and ones that point down. One of the important points in a quadratic function is the vertex. The vertex is the lowest point (minimum value) when the parabola points up and the highest point (maximum value) when it opens down. When ou can identif the vertex and the direction of the parabola, ou will be able to find minimum and maximum values of quadratic functions. Directions: Graph the following functions using our graphing calculator. Answer the questions that go along with the graphs. 1A. Graph x 1B. Graph x To graph using the 84+ calculator: 1. Press Y=. Tpe in the function. 3. Press graph 4. Press nd graph to view a table of values for the function 5. Graph at least 5 points. Describe how these two graphs are similar and different. What do ou think effected the changes in the graphs?

2 In question 1A, ou graphed the parent function for quadratic functions. Now ou will examine how quadratic functions can be translated. The function will be given to ou in vertex and standard form. When ou are graphing them in our graphing calculator, use vertex form. Graph and answer the questions below. 3. ( x ) 4. ( x 3) 4 (Standard form: x 4x 6) (Standard form: x 6x 5) Vertex: Direction: Minimum/Maximum value: Domain: Range: Vertex: Direction: Minimum/Maximum value: Domain: Range: 5. 4( x1) 6. 1 ( x 1) (Standard form: 4x 8x 6) (Standard form: x x ) 4 4 Vertex: Vertex: Direction: Direction: Minimum/Maximum value: Minimum/Maximum value: Domain: Domain: Range: Range:

3 Compare our graphs to their respective functions to answer the questions below. 7. What does the variables h and k stand for in vertex form? What effect does the value of h and k have on the parent function? Make sure to include specific details involving movement. 8. What effect does a have on our graph? Include specifics details about the sign and value. How does it affect our minimum/maximum value? What do ou notice about our a value in both standard and vertex form? 9. Look vertex form versus standard form. What can ou do to vertex form to turn our equation into standard form? 10. What formula can ou use on standard form to get the x-value of our vertex? How can ou find the -value of our vertex when it is in standard form?

4 G1. G. G3. G4. G5. G6.

5 G7. G8. E1. E. E3. 3( x 4) ( x 4) 1 ( x ) 3 E4. E5. E6. 1 ( x 1) 4 1 ( x ) 3 1 ( x 3) 1

6 E7. E8. ( x 1) 4 ( x 3) D1. D. D3. D : (, ) R :[ 1, ) D : (, ) R :[, ) D : (, ) R :[ 4, ) D4. D5. D6. D : (, ) R : (,3] D :{ x : R :{ : x R} 4} D :{ x : R :{ : x R} 1}

7 D7. D8. D :{ x : x R} D :{ x : x R} R :{ : 3} R :{ : } M1. M. M3. Minimum at -4 Axis of Smmetr at x = -1 Maximum at 4 Axis of Smmetr at x = 1 Minimum at -1 Axis of Smmetr at x = 3 M4. M5. M6. Minimum at - Axis of Smmetr at x = -3 Maximum at 1 Axis of Smmetr at x = 4 Maximum at 3 Axis of Smmetr at x =

8 M7. M8. Maximum at Axis of Smmetr at x = -4 Minimum at -3 Axis of Smmetr at x =

9 Quadratics Matching Activit Name: Date: Block: For each graph, ou will need to write the vertex. Then, fill in the table with the correct card number and letter, for each description. Graph Vertex Equation Minimum or Maximum and Axis of Smmetr Domain and Range G1 G G3 G4 G5 G6 G7 G8

10 Quadratics Matching Activit Name: Date: Block: For each graph, ou will need to write the vertex. Then, fill in the table with the correct card number and letter, for each description. Graph Vertex Equation Minimum or Maximum and Axis of Smmetr Domain and Range G1 (-3, -) E8 M4 D G (, 3) E3 M6 D4 G3 (, -3) E5 M8 D7 G4 (1, 4) E4 M D5 G5 (4, 1) E M5 D6 G6 (-1, -4) E7 M1 D3 G7 (3, -1) E6 M3 D1 G8 (-4, ) E1 M7 D8

11 Method: Get the x or the quantit squared alone on one side of the equation. Then take square root of each side, remembering that ou are solving for all possibilities and need ± in front of the square root. Finish solving for x. Method: Get the equation equal to zero. Factor. Then set each factor equal to zero and solve for x. Method: If the x term does not have a coefficient of 1, divide both sides b it. Take the coefficient of x (b). Divide it b and square the result. Add this to both sides. You can now factor one side as a quantit squared, take square root of both sides and solve for x. Method: Get the equation equal to zero. Identif a, b, and c. Substitute into the quadratic formula and simplif. When do I use it? When there is an x in the equation, but no x or when there is a quantit squared with no additional x. When do I use it? When it is possible to factor ax + bx + c. When do I use it? It can be used antime. It is easiest when a = 1 and b is divisible b. Rewrite the equation to: When do I use it? It can be used antime. It is usuall used when ax + bx + c cannot be factored.

12 Zero Square Product Completing Quadratic Root Propert (Factoring) the Square Formula Solving Quadratic Equations Algebraicall