Math 12 - Quadratics Review Question Solutions

 

1. Find the sequences of differences (D1, D2, D3, etc) for each of the following sequences to determine what type of sequence they are: 

a) {1, 28, 95, 220, 421, 716}              Solution:  This is a cubic sequence

b) {0, 15, 40, 75, 120, 175}                Solution: This is a quadratic sequence

 

2. Generate the first 6 terms for each sequence:

a) t_n = 2n² – 2n                                     Solution: {0, 4, 12, 24, 40, 60, ...}

b) t_n = n³ +5n² – 10n – 15                    Solution: {-19, -7, 27, 89, 185, 321, ...}

c) t_n = n⁴ – n²                                        Solution: {0, 12, 72, 240, 600, 1260, ...}

 

3. General to Transformational Form

 

a)              b)             c)

 

d)   e) f)

 

g)                               h)                      

 

i)                                     j)

 

k)                                           l)

 

4. Finding Roots

 

a)                  b)                  c)

 

d)     e)        f)

 

5.  Solving Equations

 

a)                  b)                  c)

 

d)                  e)         

 

f)                         g)    or                                

h)                          i)

 

6.  Calculate the discriminant

 

a)  discriminant = -47

b)  discriminant = 109

c)  discriminant = 49

d)  discriminant = 0

e)  discriminant = 81

f)  discriminant = 1

 

7. Finding the Formula of a Parabola!

To find the formula, plug the given values into the formula .

a) Vertex at (0, 0) and another point (4, 8)

h = 0, k = 0, x = 4, y = 8

Therefore,  or 

b) Vertex (2, -5) and another point (3, 1)

h = 2, k = -5, x = 3, y = 1

 

Therefore, 

c) Vertex at (-4, 3) and another point (-6, 11)

h = -4, k = 3, x = -6, y = 11

        

Therefore,

d) Vertex at (-2, 3) and another point (4, 12)

h = -2, k = 3, x = 4, y = 12

         

Therefore,