Match each equation from items 1–5 with its graph in column 2. Be sure to look
all the equations and compare them before you answer any questions. Match
equations and graphs first without using your graphing handheld, and then verify
your answers using your graphing handheld.
Note: These examples only investigate changes in the value of A.
Maximum and Minimum Values Come into Focus
When a parabola opens upward, the vertex will
be the lowest point on the curve . Any other
point on the parabola will have a larger value
for y. In the graph shown, the y-value of the
vertex is 1. This is the lowest value of y that is
on the parabola, and it is thus called the
minimum value of the function.
The graph shows a parabola with a minimum
value of 1 when x = 2.
Likewise, when a parabola opens down, the
vertex will be the maximum value for y. This
graph shows a function with a maximum value
of -3 when x = -1.
Use Your New Skill
Complete the table.
Function has a
A Quick Application
The equation y = -16(x – 4)2 + 259 models the flight of a model
rocket where y is the
height of the rocket and x is the time since it was launched. What is the
height of the rocket? How long after it was launched did it reach its maximum?
What does this have to do with this activity?
1. Use your graphing handheld to graph y = x and y = x + 3 on the same axis. In
what two ways is the second equation a translation of the first?
Now look at some functions you might not have already studied and see if you can
apply your knowledge in a new situation.
2. The graph of the function y = x3 goes
through the origin (0, 0). Look at the graph
of y = x3 shown and using the point at the
origin as the point you translate (as you did
the vertex), sketch the graph of y = x3 + 2.
Check your answer by graphing y = x3 + 2 on
your graphing handheld.
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