Download quadratic

Mathematics for Business and Economics
review of quadratic equations
1. Give the definition of quadratic equation.
2. (a)
(b)
(c)
(d)
Can
Can
Can
Can
a
a
a
a
quadratic
quadratic
quadratic
quadratic
equation
equation
equation
equation
have
have
have
have
no solution?
only one solution?
two solutions?
more than two solutions?
3. (a) What does A2 ("A squared") mean?
(b) What is the "opposite" operation (the "undo") called?
4. (a) If AB=17 , does that let you know the value of either number for certain?
If yes, what value(s) do you know? If no, why not?
(b) If AB=0 , does that let you know the value of either number for certain?
If yes, what value(s) do you know? If no, why not?
5. The quadratic equation below is not ready to solve using factoring.
2
x 26 x=120
(a) What do you need to do to the equation to get it ready?
(b) Get the equation ready for factoring. Then, solve it using factoring.
6. The quadratic equation below is not ready to solve using factoring.
w−4  w−7=10
(a) What do you need to do to the equation to get it ready?
(b) Get the equation ready for factoring. Then, solve it using factoring.
7. Each of the equations below is in the proper form for using the quadratic formula.
For each equation, give the values of the coefficients A, B, and C.
(a) 8 x 2−97 x37.2=0
(b)
(c)
(d)
(e)
3
x 298.6 x =0
4
2
3 p 21 p=0
2
17.3 R −6,000,000=0
2
z −z−42=0
8. (a) Put this equation in the proper form for solving it using the quadratic formula.
2
4z =29 z7
(b) Solve the equation using the quadratic formula.
9. Solve using any appropriate method:
10. Solve using any appropriate method:
w 2=9
3z 219 z=14
Mathematics for Business and Economics
quadratic functions in different forms
Here is a quadratic function, given in three different (equivalent) forms:
[A]
f  x =x 2−14 x 40
[B]
f  x = x−10 x−4
[C]
f  x = x−72−9
In which of these forms is it easiest
11. to find the vertex of the graph?
12. to find the x-intercepts of the graph?
13. to find the y-intercept of the graph?
14. to find the output when the input is zero?
15. to find out which input(s) will make the output zero?
16. to find out which input(s) will make the output positive?
17. to find out which input(s) will make the output negative?
18. to find out which input(s) will make the output its minimum value?
19. The process of converting from from [A] to form [B] is called...
20. The process of converting from from [A] to form [C] is called...