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Quadratic Functions
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Gravity
Key Concepts:
Terms in this set (35)
Axis of Symmetry: x = -8
y = x² + 16x + 71
Vertex: (6,10)
y = x² - 12x + 46
Axis of Symmetry: x = 2
y = -3x² + 12x
Axis of Symmetry: x = -9
y = -x² - 18x - 75
Vertex: (5,-3)
y = -3x² + 30x - 78
a is positive
If the graph opens up...
a is negative
If the graph opens down...
up, down
a tells us if the parabola opens __ or ____
minimum, maximum
a tells us if the vertex is a _______ or _________
parabola
Every quadratic function has U-shaped graph called a ______
opens down
if the leading coefficient (a) is negative, the parabola
opens up
if the leading coefficient (a) is positive, the parabola
vertex
The _____ is the lowest point of a parabola that opens up and the highest point of a parabola that opens down
axis of symmetry
the line passing through the vertex that divides the parabola into two symmetric parts called the _____ __ ________
standard form
ax^2 + bx + c = 0
parabola
vertex
axis of symmetry
Vertex (-2,-4) a=2/3
y = 2/3(x + 2)^2 - 4
Congruent to y=2/3x^2 with maximum at (-2,-4)
y= -2/3(x + 2)^2 - 4
vertex (-3, -2); passing through the point (-6, -4)
y= -2/9(x + 3)^2 - 2
vertex (1, 3) ; passing through the point (4, 5)
y = 2/9(x - 1)^1 + 3
vertex (-3, -5) ; has y -intercept of 2
y= 7/9(x + 3)^2 - 5
Find the values of a and k so the given points ( 2 , 4 ) and ( 4 , 7) lie on the graph of the parabola: y = a(x + 3)^2 + k
a = 1/8 and k = 7/8
Find the values of a and k so the given points ( -1 , -3) and ( 0 , -6) lie on the graph of the parabola: y = a(x - 1)^2 + k
a = 1 and k = -7
The sum of two numbers is 26. Find the numbers if their product is a maximum.
13 and 13
The sum of two numbers is 22, find the numbers if the sum of their squares is a minimum.
11 and 11
Cathy has 48 m of fencing to make a rectangular pen for her pet. What is the maximum area?
144 square meters
You want to construct a rectangular cattle pen having one side along an existing wall of a barn and the other three sides fenced. If you have 400 meters of fencing, what is the largest possible area your cattle pen can have?
20,000 square meters
Convert from general form to standard form. y = x^2 + 12x + 10
y = (x + 6)^2 - 26
Convert from general form to standard form. y = x^2 - 8x + 12
y = (x - 4)^2 - 4
Convert from general form to standard form. y = x^2 - 8x + 5
y = (x - 4)^2 - 11
Convert from general form to standard form. y = x^2 + 12x + 15
y = (x + 6)^2 - 21
Convert from general form to standard form. y = 2x^2 + 4x + 7
y = 2(x + 1)^2 + 5
Convert from general form to standard form. y = 2x^2 +4x - 3
y = 2(x + 1)^2 - 5
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