1.3 Maximum Or Minimum Of A Quadratic Function Worksheet - Mcgraw-Hill Education Canada Page 6
ADVERTISEMENT
1
2
3
4
5
6
7
8
9• Select 2:zero to find the x-intercepts of the function.
Tip
te c h n o l o g y
See the Use
Technology feature at
the end of this section
for a TI-Nspire
CAS
TM
graphing calculator
solution.
The zeros are approximately 0.037 and 8.2.
The solution t 5 0.037 indicates when, in the past, the ball would
have been thrown from ground level in order for it to follow the given
path. The solution t 5 8.2 indicates when the ball will return to the
ground. The ball returns to the ground 8.2 s after Jamie threw it.
b)
The maximum is midway between the two zeros. So, find the average
of the two solutions from part a).
___
0.037 8.2
5 4.0815
2
The ball will take approximately 4.1 s to reach its maximum height.
The maximum height can be found by substituting t 5 4.1 into the
c)
function.
h(t) 5 4.9t
+ 40t + 1.5
2
h(4.1) 5 4.9(4.1)
40(4.1) 1.5
2
83.13
The ball will reach a maximum height of
approximately 83.1 m.
This solution can be verified using the
maximum function on the graphing calculator.
Key Concepts
The minimum or maximum value of a quadratic function occurs at the vertex of the parabola.
The vertex of a quadratic function can be found by
– graphing
– completing the square: for f (x) 5 a(x h)
2
k, the vertex is (h, k)
_
_
(
)
x b
k, the x-coordinate of the vertex is b
– partial factoring: for f (x) 5 ax
a
2a
The sign of the coefficient a in the quadratic function
y
f (x) 5 ax
bx c or f (x) 5 a(x h)
k determines
2
2
whether the vertex is a minimum or a maximum.
If a 0, then the parabola opens upward and has a minimum.
a � 0
a � 0
If a 0, then the parabola opens downward and has a maximum.
x
0
30 MHR • Functions 11 • Chapter 1
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education