Quadratic Functions Review Chapter 2

							Quadratic Functions Review                                                   Chapter 2
PM 11
Also try review in text on P.148

1. Graph (on graph paper) and label. Find the: a) vertex, b) y-intercepts c) zeroes d)
   equation of axis of symmetry and e) domain & range of each graph.
        () (             )
                             2
    i. f x = x + 2 − 3
   ii. y = −2x 2 + 6
        ()
   iii. f x = 2x 2 − 4x − 7

2. Solve the following:
   a. x 2 − 6x − 40 = 0
   b. 3x 2 − 5x − 8 = 0
   c. 4x 2 − 11x − 3 = 0

3. Write the equation of a quadratic function having the following pair of roots:
   a. 4, − 2
       1
   b.    ,6
       3
       2     3
   c.    , −
       3     5

4. What is the equation of a parabola with vertex (0, 4) and passing through (1, 6).

                                                                 (       )
5. Write the equation of a quadratic function with vertex −2, − 5 and y-intercept 3.

6. The parabola y = x 2 is vertically expanded by a factor of 3 and translated 4 units
   down and 2 units right. What is the equation of the new parabola in
         (     )
                   2
   y =a x−p            + q form?


                                               (     )
                                                         2
7. Change the following into standard y = a x − p            + q form.
   a. y = x 2 + 2x + 7
        ()
   b. f x = −2x 2 + 8x − 1
   c. y = 4x 2 − 24x + 25

8. A rocket is launched into the air. Its height over time is given by y = −2t 2 + 12t
   where h is the height in metres, and t is the time in seconds.
   a. Graph on graph paper and label.
   b. Find the maximum height.
   c. Find the domain and range.
   d. What is the height of the rocket after 2.5 s?
   e. For how long is the rocket above a height of 13 m?
9. A flowerpot is thrown from a window. Its height over time is given by:
        ()
   h t = −4.9t 2 + 20t + 18 where h is the height in m, and t is the time in seconds.
   a.    Sketch a graph based on your graphing calculator and label.
   b.    What is the maximum height of the flowerpot?
   c.    Find the domain.
   d.    When does the flowerpot reach a height of 40m?

10. The sum of two natural numbers is 14. Their product is a maximum. What are
    the numbers? Solve algebraically.

11. A rectangular pen borders a river. If the three sides require 120 m of total
    fencing, what dimensions will yield the maximum area?

12. Two numbers have a difference of 34. What is the sum of their squares if it is a
    minimum? What are the numbers?

13. Find the equation of the inverse for the following functions. Graph one line and
    one quadratic function and their inverses.
    a. y = 5x + 1
              1
           ()
    b. f x = x − 4
              3
         f ( x ) = ( x − 3) + 3
                          2
   c.

         y = ( x + 2) + 3
                      2
   d.


                  (       )
                              2
14. Graph y = x + 2 − 5 and its inverse, but restrict the domain to ensure that the
   inverse is also a function.

                                    (     )                   (      )
15. Graph the parabola with vertex −2, 0 , passing through −4, 4 and 0, 4 .(       )
   Graph its inverse on the same grid. Label graphs.

                                               (      )      ( )
16. Graph the linear function passing through 0, − 3 and 2, 1 , and its inverse on
   the same grid. Label graphs.