PAP Algebra II
Notes 4.3 Three Forms of the Quadratic
EXPLORE:
In your calculator graph:
1) y = 3( x − 4)( x + 2)
30-
What do the 4 and 2 represent
on the graph?
____________________________
2) y = 3( x − 1) 2 − 27
-10
10
What do the 1 and 27 represent
on your graph?
____________________________
3) y = 3 x 2 − 6 x − 24
-30What does the -24 represent
on your graph?
____________________________
All of these are different equations for the same parabola.
FACTORED FORM: F ( x) = a( x − r1 )( x − r2 ) where r1 and r2 are roots (i.e zeros
or x-intercepts) of the parabola.
2
VERTEX FORM: V ( x) = a ( x − h) + k where the vertex is the point (h, k ) .
2
STANDARD FORM: S ( x ) = ax + bx + c where c is the y-intercept.
1) Put the following equations in standard form:
a) y = 3( x − 1)( x + 4)
c) y = 2( x − 3) 2 + 1
b) y = −( x + 2)( x + 3)
d) y = −3( x + 4) 2 − 5
2) Graph the given data and then write the equation for the quadratic in the three
forms we have learned. (F is factored form, V is vertex form, and S is standard form)
Vertex:
(3, -4)
Roots:
(1, 0) and (5, 0)
Y- intercept: (0, 5)
a=1
F(x) =
V(x) =
S(x) =
3) A toy rocket takes off from the ground and peaks 1600 feet off the ground after 10
seconds. Graph this situation and label significant points.
a) What value are you missing in order
to write your three equations?
b) Write the vertex and factored forms and use
an “a” for the a value.
c) How can you find the value of a? Find the value of a.
d) What are two forms of the equation for this situation with the a value substituted?
e) What is a reasonable doman and range for this situation?
f) Over what intervals is the graph increasing/decreasing?
4) A baseball is thrown from 5 feet above the ground. The ball reaches a maximum height
of 9 feet after 2 seconds. The ball lands on the ground 5 seconds after it was thrown.
F(x) =
V(x) =
S(x) =
Reasonable Domain:
Reasonable Range:
Over what interval is the graph increasing? Over what interval is the graph decreasing?

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