Lesson on Plotting Cubic Graphs

Introduction

• Focus on plotting the equation: ( y = x^3 )
• Graphs require understanding of both x and y values
• Example provided: Solving ( 5 = x^3 )

Steps to Plotting ( y = x^3 )

1. Calculate Points

   • ( x = 0: y = 0^3 = 0 )
     • Plot (0, 0)
   • ( x = 1: y = 1^3 = 1 )
     • Plot (1, 1)
   • ( x = 2: y = 2^3 = 8 )
     • Plot (2, 8)
   • ( x = -1: y = (-1)^3 = -1 )
     • Plot (-1, -1)
   • ( x = -2: y = (-2)^3 = -8 )
     • Plot (-2, -8)

2. Draw the Graph

   • Connect these points with a smooth curve.

3. Solve using Graph

   • Equation: ( 5 = x^3 )
   • Draw horizontal line ( y = 5 ), find intersection
   • Vertical line from intersection to x-axis gives solution
   • Approximate solution: ( x \approx 1.75 )

Additional Exercise: Plot and Solve ( y = x^3 - 5 )

Steps to Plot

1. Calculate Points

   • ( x = 0: y = 0^3 - 5 = -5 )
     • Plot (0, -5)
   • ( x = 1: y = 1^3 - 5 = -4 )
     • Plot (1, -4)
   • ( x = 2: y = 2^3 - 5 = 3 )
     • Plot (2, 3)
   • ( x = -1: y = (-1)^3 - 5 = -6 )
     • Plot (-1, -6)
   • ( x = -2: y = (-2)^3 - 5 = -13 )
     • Plot (-2, -13)

2. Draw the Graph

   • Connect these points with a smooth curve.

3. Solve using Graph

   • Equation: ( 3 = x^3 - 5 )
   • Draw horizontal line ( y = 3 ), find intersection
   • Vertical line from intersection to x-axis gives solution
   • Solution: ( x = 2 )

Conclusion

• Successfully learned plotting cubic graphs
• Utilized graphs for solving equations
• Interactive component suggested for practice

Thank you for watching and participating!