Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 7
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
114
Representing a quadratic function in
EXAMPLE
factored and standard forms from a graph
From the graph of this quadratic function,
f(x)
8
determine the function’s factored and
(4, 6)
6
standard forms.
4
2
x
2 0
4
2
4
6
2
4
6
8
Randy’s Solution
f (x) 5 a(x 2 r)(x 2 s)
A quadratic function can be written
in the form f(x) 5 a(x 2 r) (x 2 s),
f (x) 5 a(x 2 (22))(x 2 (13))
where r and s are the zeros of
f (x) 5 a(x 1 2)(x 2 3)
the function and a indicates the
shape of the parabola. From the
graph, the zeros are x 5 22 and
x 5 3. I substituted 22 for r and 3
for s, then simplified.
Let (x, y) 5 (4, 6)
To get a, I picked any point on the
6 5 a(4 1 2)(4 2 3)
curve, substituted its coordinates
6 5 a(6)(1)
into the function, and then solved
for a.
a 5 1
I used my value of a to rewrite the
f (x) 5 1(x 1 2) (x 2 3)
function in factored form.
f (x) 5 1(x
2 3x 1 2x 2 6)
2
I expanded to get the standard
f (x) 5 x
2 x 2 6
2
form.
From the graph the y-intercept of
the parabola is 26. This is also
seen in the function when
it’s written in standard form.
138
Chapter 3
NEL
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education