Download Investigation: Finding the Vertex

Name:
Date:
Math 2
Investigation: Finding the Vertex
1. Graph each of these functions on your calculator, and find the vertex using the maximum or minimum
command in your calculator. Look for a pattern in the answers. At the end you’ll be asked to identify
the pattern.
a. f(x) = 2(x – 5)2 + 3.
vertex:
b. f(x) = –3(x – 4)2 + 5.
vertex:
(x – 5)2 – 8.
vertex:
c. f(x) =
1
2
d. f(x) = (x + 1)2 – 6.
vertex:
f. f(x) = (x – 4)2 – 16.
vertex:
(you’ll need to adjust
the window to see the
vertex)
Name:
Date:
Math 2
2. Look for a pattern in the answers to problem 1. Use the pattern to answer these questions.
a. Without your calculator, guess the location of the vertex of h(x) = 3(x – 2)2 + 5.
Then check it by graphing on your calculator
b. At what x value does f (x ) = (x - 2) have its minimum? Explain how you know.
2
c. Fill in the following table. Are the results consistent with your answer to part b?
–2
x
–1
0
1
2
3
4
g(x) = x 2
f (x ) = (x - 2)
2
d. If the vertex of a parabola is the point (3, 4), then a possible equation for the parabola could be:
f (x ) =
e. . If the vertex of a parabola is the point (–3, –4), then a possible equation for the parabola could be:
f (x ) =
f. If the vertex of a parabola is the point (h, k ), then a possible equation for the parabola could be:
f (x ) =