Quartics Investigation 1. Sketch the following graphs with the help of your graphics calculator. Use a separate set of axes for each. a) y x 4 b) y 3x 4 c) y 2 x 4 d) y ( x 1)4 3 e) y 2( x 1)4 2 2. Use your knowledge from 1. to explain the shape of graphs in the form y a ( x h) 4 k 3. Sketch the following graphs with the help of your graphics calculator. Use a separate set of axes for each. a) y x( x 1)( x 2)( x 3) b) y 2 x( x 1)( x 2)( x 3) c) y ( x 5)( x 3)( x 2)( x 1) 4. Comment on the nature of the graphs found in the form y a( x b)( x c)( x d )( x e) 5. Investigate further to find a general rule for a quartic graph with 2 turning points on the x-axis. 6. Sketch two different quartic graphs with a point of inflexion on the x-axis. How many other x-intercepts are possible? Write a general rule for this type of function. 7. Sketch a quartic graph with one x-intercept only. Find a general rule for a function of this type. Challenge: 1. How many different quartic graph shapes are possible? 2. Sketch a graph with a point of inflexion on the x-axis, a turning point on the xaxis, and one other x-intercept. Write a rule for this function.