Algebra 2 Name ______
Review – Unit 3 –Quadratics
Use the graph to determine the number and type of solutions of the quadratic equation.
1) 2) 3)
How many Solutions? ______How many Solutions? ______How many solutions? ______
Type (circle): Real or Imaginary Type (circle): Real or Imaginary Type (circle): Real or Imaginary
Simplify each expression. Leave answer in radical form.
4) 5) 6)
Simplify each expression.
7) (3 + 4i) – (7 – 2i) 8) (5 – i)(9 + 6i) 9) (3 + 8i) + (5 – 2i)
10) 4i(7 + 8i) 11) (4 + 6i)(2 + i) 12) (-5i)(-10i)
Solve each equation by factoring.
13) x2 – 12x + 32 = 0 14) x2 + 2x – 8 = 0 15) 2x2 + 11x + 12 = 0
Solve each equation by finding square roots.
16) 4(x – 2)2 + 2 = 34 17) x2 – 9 = 0 18) 5x2 - 40 = 80
Solve by using the Quadratic Formula.
19) 20) x2 + 3x + 5 = 0
Solve by completing the square.
21) x2 + 6x – 7 = 0 22) x2 - 4x = -29
23) Using the graph below, graph each equation and state the
coordinates of all the points that are solutions to the system.
y = (x – 3)2 - 4
y = -2x + 5
24) For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is given by
a) What is the value of the y-intercept? What does this mean in the context of the problem?
b) How long does it take the rocket to reach its maximum height?
c) What is the maximum height of the rocket?
c) How long does the rocket travel horizontally before it hits the ground?
Evaluate a) the discriminant of each equation and b) how many real and imaginary solutions does each have?
22) x2 + 6x – 7 = 0 23) 3x2 – x + 3 = 0
Discriminant = ______Discriminant = ______
a. 2 real, 0 imaginary a. 2 real, 0 imaginary
b. 1 real, 0 imaginary b. 1 real, 0 imaginary
c. 0 real, 2 imaginary c. 0 real, 2 imaginary
Graph the inequality. Don’t forget to shade. Graph the systems of inequalities.
24) 25)
26) Solve the system by elimination.
27) Solve the system by substitution AND graph it to show that your solution is the same.
By Substitution: By Graphing:
28) Elijah is dropping water balloons from a window that is 200 ft high. The equation models the height f(t) (in feet) of an object t seconds after it is dropped from the window.
a) After how many seconds will the object hit the ground?
b) What is the height of the water balloon 2.5 seconds after it has been dropped from the top of the tower?