1.3 Maximum Or Minimum Of A Quadratic Function Worksheet - Mcgraw-Hill Education Canada Page 3
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9Investigate B
tools
• graphing calculator or
How can you use partial factoring to find a minimum or a maximum?
grid paper
.
Graph the function f (x) 5 2x
4x.
2
How many x-intercepts does this function have?
.
3.
Use the x-intercepts to find the vertex of the parabola.
4.
Graph the functions g(x) 5 2x
4x 2 and h(x) 5 2x
4x 5 on
2
2
the same set of axes as f (x).
5.
How many x-intercepts does g(x) have? h(x)?
6.
Describe how to find the vertex of the new parabolas, g(x) and h(x),
based on the vertex of the original parabola, f (x).
Reflect
7.
Using your answer from step 6, suggest a method that can be
used to find the maximum or minimum of a parabola of the form
f (x) 5 2x
4x k for any value of k.
2
example 2
Use Partial Factoring to Find the Vertex of a Quadratic Function
Find the vertex of the function y 5 4x
12x 3 by partial factoring. Is
2
the vertex a minimum or a maximum value? Explain.
Solution
Work with the function y 5 4x
12x to find the x-coordinate of the
2
vertex, since the x-coordinate of the vertex of y 5 4x
12x 3 will be
2
the same.
y 5 4x(x 3)
Co nne c tio ns
For y 5 0:
0
5 4x(x 3)
The vertex of a
quadratic function
4x 5 0 or x 3 5 0
Use the zero principle. If AB = 0, then either A = 0 or B = 0.
is on the line of
symmetry, which is
x 5 0 or
x 5 3
These give the x-intercepts of the function y = 4x
— 12x.
2
halfway between the
x-intercepts.
The average of these two x-intercepts will give the x-coordinate of the
vertex for y 5 4x
12x and y 5 4x
12x 3:
2
2
y
__
_
0 3
5 3
2
2
r
s
x
0
1.3 Maximum or Minimum of a Quadratic Function • MHR 7
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