9.2 Graph and Write Equations of Parabolas

Goal  Graph and write equations of parabolas that open left or right.

Your Notes

VOCABULARY
Focus
A fixed point that lies on the axis of symmetry of a parabola

Directrix
A line that is perpendicular to the axis of symmetry of a parabola

STANDARD EQUATION OF A PARABOLA WITH VERTEX AT THE ORIGIN
The standard form of the equation of a parabola with vertex at (0, 0) is as follows:

Equation	Focus	Directrix	Axis of Symmetry	
x2 = 4py	(0, p)	y = __p__	Vertical (__x = 0__)	
y2 = 4px	(p, 0)	x = __p__	Horizontal (__y = 0__)	

Your Notes

Example 1
Graph an equation of a parabola

2

2

1

y

Graph x =	. Identify the focus, directrix, and axis of symmetry.
1.	Rewrite the equation in standard form.

2

2

1

y

x =	Write original equation.	
__2x__ = __y2__	Multiply each side by __2__.	

2.	
2

1

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2

1

÷

÷

ø

ö

ç

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0

,  

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1

Identify the focus, directrix, and axis of symmetry. The equation has the form y2 = 4px where P =___.focus is (p, 0), or	. The directrix is x = p, or x = _____.Because y is squared, the axis of symmetry is the __x–axis__ .

3.	Draw the parabola by making a table of values and plotting points. Because p _>_ 0, the parabola opens to the __right__. So, use only __positive__ x–values.

x	1	2	3	4	5	
y	__1.41__	__2__	__2.45__	__2.83__	__3.16__	

Checkpoint Complete the following exercise.

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4

1

x

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1.	Graph y =	.Identify the focus, directrix, and axis of symmetry.
focus: (0, 1); directrix:
y = 1; axis of symmetry:
y–axis, x=0

Your Notes

Example 2
Write an equation of a parabola

Write an equation of the parabola shown.

Solution
The graph shows that the vertex is__(0, 0)__ and the directrix is y = p =__3__. Substitute __3__ for p in the standard form of the equation of a parabola.

x2 = 4py	Standard form, __vertical__ axis of symmetry	
x2 = 4(3)y_	Substitute for p.	
_x2 = 12y_	Simplify.	

Checkpoint Complete the following exercise.

2.	
4

3

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=

x

Write the standard form of the equation of the parabola with vertex at (0, 0) and the directrix
.
y 2 = 3 x

Homework
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