Graphical And Three Symbolic Forms Of A Quadratic Function Worksheet
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1
2
3
4Graphical and Three Symbolic Forms of a Quadratic Function
Part 2 – Standard (General) Form
Name ___________________________
2
Definition: The standard form of a quadratic function is given as:
f x
( )
ax
bx c
, where a, b, & c are real
numbers.
8. Graph each of the following on a graphing calculator.
2
2
2
t x
( )
x
3
x
10
r x
( )
x
14
x
13
u x
( )
x
11
x
28
2
v x
( )
x
2
x
5 25
.
9. Identify the roots for each of the above functions.
t(x) ___________
r(x) ___________
u(x) ___________
v(x) ___________
10. How do the roots in #9 compare with the roots of functions in #1 from part 1?
11. Based on your observations, how can you convert the equations from #1 into those given in #8? Use your
graphing calculator to check your hypothesis.
Part 3 – Vertex Form
2
f x
( )
a x h
(
)
k
Definition: Another form of a quadratic function, known as vertex form, is given as:
, where h
& k are real numbers.
Let’s take a closer look at this form. Remember the vertex of a parabola is either the minimum or the maximum point
of the function.
12. Graph each of the following functions and identify the vertex of each using the calculator.
2
2
2
f x
( )
(
x
) 2
3
g x
( )
(
x
) 4
5
h x
( )
(
x
35
. )
0 25
.
1
2
2
2
i x
( )
(
x
15
. )
4
j x
( )
(
x
2
)
6
k x
( )
1
(
x
7 5
. )
3 25
.
2
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