quadratic functions powerpoint for eleven graders

quadratic functions

1. 11 TH GRADE QUADRATIC FUNCTIONS BY:Yasemin,Noor Aslan,lemar,yumna

2. Hello everyone, your friend lemar did some researches about quadratic functions lets go and explore them together,...

3. Before, i want to start with a question…

4. "Can quadratic functions predict if a cat will knock over a glass of water? "

5. Well let's start with quadratic functions then at the end we will know ;)..

6. Researches and exploration 03 04 01 02 Mini experiment Graph and hidden secrets Project Journal TABLE OF CONTENTS

7. Research and exploration 01

8. WHAT IS QUADRATIC EQUATIONS? A quadratic function is a type of polynomial function of degree 2, meaning its highest degree term is squared. F (x)= ax^2 + bx + c . A, B and C are constant ( coefficient ) . X represents the variable . AX^2 is the quadratic term . BX is the linear term . C is the constant term

9. The quadratic function graph is a parabola, and its direction of opening depends on the sign of the coefficient a. If a > 0, the parabola opens upward; if a < 0, it opens downward. Many real-world phenomena, including projectile motion, optimisation issues, engineering designs, and more, are frequently modelled using quadratic functions. They are essential to mathematics and have several uses in other disciplines. Parabola and projectile motion

10. When it comes to explaining the velocity of projectiles, including things hurled, rockets launched, and even the motion of astronomical bodies, quadratic functions are essential. Let us investigate the mathematical enigmas surrounding projectile motion and examine the insights and patterns provided by quadratic equations. Projectile motion

11. Projectile motion Equations of Motion: Two distinct motions are usually taken into account when analysing projectile motion: vertical motion (influenced by gravity) and horizontal motion (affected by initial velocity and no acceleration). The following equations control these motions: horizontal motion: x + x0 + v0x . t vertical motion: y + y0 + v0y . t - ½ gt^2 Combining equations: We combine the horizontal and vertical motions to describe the projectile's whole trajectory. Given that there is no air resistance and no acceleration in the horizontal direction, the horizontal motion is uniform, as shown by the formula x + x0 + v0x. t In the meantime, gravity has an impact on vertical motion, which leads to the quadratic equation for vertical position.

12. Projectile motion 3. Quadratic Equation for Projectile Motion: The following results from entering the horizontal motion equation expression for x into the vertical motion equation: y + y0 + v0y . t - ½ gt^2 substituting V0X . cos(0) and V0Y= V0 . sin(0) where V0 is the initial velocity and 0 is the launch angle we can write the equation as: y=y0 + ( v0 . sin(0) ) . t - ½ gt^2 This equation represents the vertical motion of a projectile launched at an angle 0 with an initial velocity V0 Like the purr-mission!"

13. Projectile motion 4. Trajectory and Maximum Height: The projectile's trajectory is a parabola, and when the vertical velocity drops to zero, it reaches its maximum height. It is possible to calculate the time to attain maximum height (tmax) and (ymax) by using calculus or other methods. 5. Range: By taking into account the horizontal velocity (V0X) and the overall time of flight (t flight), quadratic equations can also be used to calculate the projectile's range, or horizontal distance travelled. By means of these mathematical examinations, we reveal the complex relationships and understandings that regulate projectile motion, all contained within the graceful structure of quadratic equations.

14. Mini experiment 02

15. GRAPH THis is our graph We found that the Height is(Max point) 5.5 cm Distance is 12.5 cm Time is 2.3 sec x-intercept=(-1.7,0) Y-intercept=(0,3)

16. MINI EXPIREMENT

17. Visual Graph 12.5 5.5

18. REAL GRAPH

19. Video Add it here

20. Project Journal 05

21. In our project, we immerse ourselves in the realm of everyday mathematics, where the motion of ordinary objects reveals the beauty of quadratic equations and projectile motion. Through a simple experiment of tossing a ball into the air, we uncover the intricate dance of projectile motion, a phenomenon exemplified by the ball's graceful ascent and inevitable descent. Beginning with an overview of quadratic equations and their connection to parabolic graphs, we delve into the nuances of projectile motion, uncovering its five essential types . Through meticulous analysis and our mini-experiment ( the ball experiment) , we unveil the intricate relationships governing projectile motion, bridging theory with practical observation to reveal the graceful dance of objects through the air. Our project not only illuminates the elegance of mathematics in action but also underscores its indispensable role in understanding and shaping the world around us. In conclusion :

22. Thanks