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!
- Examine this quadratic function:
y= (x− 3)(4x− 1)
Does the parabola representing the graph of this function open upward or downward? - What are the real zeros, if any, of the function stated in Prob. 1?
- What are the coordinates of the point representing the extremum of the function stated
in Prob. 1? - Draw an approximate graph of the function stated in Prob. 1.
- 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 - What are the coordinates of the vertex point on the parabola representing the function
stated in Prob. 5? - 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? - What are the real zeros, if any, of the function stated in Prob. 7?
- What are the coordinates of the point representing the vertex of the parabola for the
function stated in Prob. 7? - Draw an approximate graph of the function stated in Prob. 7.