Standardized Test Practice

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EXAMPLE 1
Standardized Test Practice
SOLUTION
Let ( x1, y1 ) ( 3, 5) and ( x2, y2 ) ( 4,
1 ).
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EXAMPLE 2
Classify a triangle using the distance formula
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EXAMPLE 3
Find the midpoint of a line segment
SOLUTION
Let ( x1, y1 ) (5, 1) and ( x2, y2 ) ( 1, 6
).
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EXAMPLE 4
Find a perpendicular bisector
SOLUTION
(1, 5)
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EXAMPLE 4
Find a perpendicular bisector
STEP 2
4
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EXAMPLE 4
Find a perpendicular bisector
y 5 4(x 1),
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EXAMPLE 5
Solve a multi-step problem
Asteroid Crater
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EXAMPLE 5
Solve a multi-step problem
SOLUTION
y x 34
y 3x 110
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EXAMPLE 5
Solve a multi-step problem
y x 34
Write first equation.
3x 110 x 34
Substitute for y.
4x 76
Simplify.
x 19
Solve for x.
y ( 19) 34
Substitute the x-value into the first equation.
y 53
Solve for y.
The center of the circle is C ( 19, 53).
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EXAMPLE 5
Solve a multi-step problem
Use (x1, y1) (0, 0) and (x2, y2) (19, 53).
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EXAMPLE 1
Graph an equation of a parabola
Graph x y2. Identify the focus, directrix,
and axis of symmetry.
SOLUTION
Write original equation.
Multiply each side by 8.
8x y2
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EXAMPLE 1
Graph an equation of a parabola
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EXAMPLE 1
Graph an equation of a parabola
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EXAMPLE 2
Write an equation of a parabola
SOLUTION
x2 4py
Standard form, vertical axis of symmetry
x2 6y
Simplify.
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EXAMPLE 3
Solve a multi-step problem
Solar Energy
Write an equation for the EuroDishs cross
section with its vertex at (0, 0).
How deep is the dish?
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EXAMPLE 3
Solve a multi-step problem
SOLUTION
STEP 1
Write an equation for the cross section. The
engine is at the focus, which is p 4.5
meters from the vertex. Because the focus is
above the vertex, p is positive, so p 4.5. An
equation for the cross section of the EuroDish
with its vertex at the origin is as follows
x2 4py
Standard form, vertical axis of symmetry
x2 4(4.5)y
Substitute 4.5 for p.
Simplify.
x2 18y
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EXAMPLE 3
Solve a multi-step problem
STEP 2
x2 18y
Equation for the cross section
(4.25)2 18y
Substitute 4.25 for p.
Solve for y.
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EXAMPLE 3
Solve a multi-step problem