Mixed Review - Power and Polynomial Functions Name:
Alg2 CC
1) Graph each function by finding the x and y intercepts and thinking about end-behavior. Then solve the inequality graphically by shading.
a) b)
2) Solve each of the following quadratic inequalities. Write your final answers in set-builder notation AND represent the solution set on a number line.
3) A ball is thrown straight upward where its height h meters above the ground after t seconds is given by . Answer the questions below. Show and/or describe all your work.
Round all times to the nearest tenth of a second and all heights to the nearest tenth of a meter.
a) When does the ball hit the ground?
b) Find the time interval when the ball is at least 300 meters above the ground.
Factoring Fun! Factor completely each polynomial expression below. Remember: These are just expressions, not equations. So we’re not solving anything; we’re just factoring.
4) Factor: 5) Factor:
6) Factor: 7) Factor:
8) Factor: 9) Factor:
Solve each equation below algebraically. (Remember: On the test, if you can’t solve using the strategy asked for, solve the equation using another strategy. You’ll at least get partial credit as long as you show your work clearly!)
10)
11)
Solve each equation below algebraically.
12) 13)
14) 15) Solve over the set of complex numbers:
16) Describe how the parent function was transformed below.
Parent function: transformed function: Describe transformation:
17) Write a polynomial equation in standard form with the given roots and point on the graph.
a) x-intecepts: ,
y-intercept:
b) roots:
point on curve:
Write the polynomial in factored form.
c) double root at, roots are and
point on graph:
18) Now make a sketch of each function you wrote above without using your calculator! Clearly mark x-intercepts and show end behavior.
19) Re-write each quadratic equation below so that you can clearly see how has been transformed. In other words, write in the form . Then describe how the parabola has been transformed.
a)
b)