Quadratic Functions Worksheet - Lesson 36 Ma 152, Section 3.1, Purdue Math Page 3
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8Standard Equation for a Parabola:
If the vertex of a parabola is (h, k) and the parabola opens upward or downward, the standard equation
. If a is positive, the parabola opens upward, negative it
2
of the parabola has the form
y a x h
(
)
k
opens downward.
Ex 2: For each parabola, find :
The standard form of the equation of the
1)
The vertex
parabola that was graphed in Ex. 1 is
2)
Equation for the axis of symmetry
1
.
2
y
(
x
1)
2
3)
Direction of opening
2
4)
Domain and range
5)
y-intercept
6)
A point corresponding to the y-intercept that has the same y-coordinate
2
a
)
f x
( ) 2(
x
4)
6
1
2
b
)
f x
( )
(
x
2)
4
From the process on page 2, you can see that the coordinates of the vertex can be found from the general
form by the following equations.
b
h
2
a
2
b
k
c
4
a
Rather than finding k by using the formula above, it is easier to substitute the value of h for x in the
quadratic equation and solve for y.
k
f h
( )
3
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