QUADRATIC FUNCTION MATH FORM 4 KSSM 2021 DISCUSSION PART 1

MATH FORM 4

1. CHAPTER 1 QUADRATIC FUNCTION AND EXPRESSION IN ONE VARIABLE MATHEMATICS FORM 4 KSSM PREPARED BY TEACHER_AZLINA

2. The image below shows a motor cycle jumping a ramp. What ‘shape’ is the path that the moto cycle follows? The shape of this movement is a parabola. Do you know that this parabola has its own equation? parabola

3. Identify And Describe The Characteristics Of Quadratic Expressions In One Variable A quadratic expression in one variable is an expression whereby the highest power for the variable is two . All quadratic expressions can be written in the form of ax 2 + bx + c , where a , b and c are constants and , x is a variable .   Determine whether each of the following expressions is a quadratic expression in one variable. If not, justify your answer. Quadratic expression in one variable Not a quadratic expression in one variable             The highest power of the variable is 3. There are two variable, x and y. There is a variable with a power which is not a whole number. Example 1

4. State the values of a, b and c for each of the following quadratic expressions. Example 2 Identify And Describe The Characteristics Of Quadratic Expressions In One Variable A quadratic expression in one variable is an expression whereby the highest power for the variable is two . All quadratic expressions can be written in the form of ax 2 + bx + c , where a , b and c are constants and , x is a variable .   (a) (b) (c) (d) (e) (f) (a) (b) (c) (d) (e) (f) a = b = c =   a x 2 + b x + c 3 –4 5 a = b = c =   –2 8 a = b = c = –1 7 a = b = c = 3 –15 a = b = c =     a = b = c =    

5. Determine the different between quadratic function and quadratic expression Determine whether each of the following is a quadratic function or quadratic expression. A quadratic expression is written in the form of + bx + c , a ≠ 0 . Q uadratic function is written in the form of f ( x ) = + bx + c . Represented by a graph .   (a) 3   (b) (c) (d) 3k ( k-5) (a) (b) (c) (d) 3k ( k-5) Example 3 Quadratic Expression Quadratic Function

6. x x Number of points of intersection = 2 Points of intersection = (-1 , 4) (4 , 4) Recognise quadratic function as many-to-one relation, hence, describe the characteristics of quadratic functions. Use horizontal line to determine whether a function is one-to-one or many-to-one Intersection point

7. x x Number of points of intersection = 2 Points of intersection = (-1 , 4) (4 , 4) Recognise quadratic function as many-to-one relation, hence, describe the characteristics of quadratic functions. Use horizontal line to determine whether a function is one-to-one or many-to-one The type of relation of a quadratic function is a many-to-one relation. x f(x) -1 4 4 4 Intersection point

8. x x Number of points of intersection = 2 Points of intersection = (0 , 1) (4 , 1) Recognise quadratic function as many-to-one relation, hence, describe the characteristics of quadratic functions. Use horizontal line to determine whether a function is one-to-one or many-to-one

9. Number of points of intersection = 2 Points of intersection = (0, 1) (4 , 1) Recognise quadratic function as many-to-one relation, hence, describe the characteristics of quadratic functions. Use horizontal line to determine whether a function is one-to-one or many-to-one The type of relation of a quadratic function is a many-to-one relation. x f(x) 4 1 1 x x

10. Describe the characteristics of quadratic functions. For a graph of f ( x ) = ax 2 + bx + c , a ≠ 0 there are only two shapes of the graphs, the value of a determines the shape of the graph. if a > 0, vertex (h, k) is minimum point (d) if a < 0 vertex (h, k) is maximum point Click the link below and drag the slider to show the animation of the graph shape change based on the value of a https://www.geogebra.org/graphing/pp5dvf8v The graph of f is a parabola with vertex ( h , k ). a < 0. a > 0. Minimum point Maximum point

11. Describe the characteristics of quadratic functions. there are only two shapes of the graphs and the value of a determines the curve shape of the graph. if a > 0, vertex (h, k) is minimum point if a < 0 vertex (h, k) is maximum point Value of a Shape of graph Maximum/minimum point and coordinates Axis of symmetry Example 4 Complete the table below for the following function. (a)     a < 0. a > 0. Open Up @ smile Minimum point (6, –8) Axis of symmetry parallel to the y-axis and passes through the maximum or minimum point.   1.5 10.5    

12. Describe the characteristics of quadratic functions. there are only two shapes of the graphs and the value of a determines the curve shape of the graph. if a > 0, vertex (h, k) is minimum point if a < 0 vertex (h, k) is maximum point Value of a Shape of graph Maximum/minimum point and coordinates Axis of symmetry Example 4 Complete the table below for the following function. (b)     a < 0. a > 0. Open down @ sad Maximum point (3, 10) Axis of symmetry parallel to the y-axis and passes through the maximum or minimum point.   –0.15 6.15    

13. Describe the characteristics of quadratic functions. there are only two shapes of the graphs and the value of a determines the curve shape of the graph. if a > 0, vertex (h, k) is minimum point if a < 0 vertex (h, k) is maximum point Value of a Shape of graph Maximum/minimum point and coordinates Axis of symmetry Example 4 Complete the table below for the following function. (c)     a < 0. a > 0. Open up @ smile Minimum point (3, 4) Axis of symmetry parallel to the y-axis and passes through the maximum or minimum point.       The coordinate and the equation of the axis of symmetry can be find using:        

14. Describe the characteristics of quadratic functions. there are only two shapes of the graphs and the value of a determines the curve shape of the graph. if a > 0, vertex (h, k) is minimum point if a < 0 vertex (h, k) is maximum point Value of a Shape of graph Maximum/minimum point and coordinates Axis of symmetry Example 4 Complete the table below for the following function. (d)     a < 0. a > 0. Open down @ sad Maximum point   Axis of symmetry parallel to the y-axis and passes through the maximum or minimum point.       The coordinate and the equation of the axis of symmetry can be find using: