Algebra Know-It-ALL

412 Graphs of Quadratic Functions

y= 2 x^2 + 4 x+ 3

= 2 × 12 + 4 × 1 + 3

= 2 + 4 + 3

= 9

The third point is therefore (1, 9). We now have three points on the curve: (−3, 9), (−1, 1), and (1, 9).

Figure 24-10 shows these points along with an approximation of the parabola passing through them.

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems.

Don’t hurry! You’ll find worked-out answers in App. C. The solutions in the appendix may

not represent the only way a problem can be figured out. If you think you can solve a particu-

lar problem in a quicker or better way than you see there, by all means try it!

1. Examine this quadratic function:
   y= (x− 3)(4x− 1)
   Does the parabola representing the graph of this function open upward or downward?


2. What are the real zeros, if any, of the function stated in Prob. 1?


3. What are the coordinates of the point representing the extremum of the function stated
   in Prob. 1?


4. Draw an approximate graph of the function stated in Prob. 1.


5. The graph of the following quadratic function lies entirely above the x axis. How can
   we know this without plotting any points?
   y= 7 x^2 + 5 x+ 2


6. What are the coordinates of the vertex point on the parabola representing the function
   stated in Prob. 5?


7. Consider the following quadratic function:
   y=− 2 x^2 + 2 x− 5
   Does the parabola representing the graph of this function open upward or downward?


8. What are the real zeros, if any, of the function stated in Prob. 7?


9. What are the coordinates of the point representing the vertex of the parabola for the
   function stated in Prob. 7?


10. Draw an approximate graph of the function stated in Prob. 7.