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maths
Parabolas
Analyze the graph and determine its standard form
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y=3(x2)+2y=3\left(x^2\right)+2y=3(x2)+2
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y=(x−3)2+2y=\left(x-3\right)^2+2y=(x−3)2+2
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y=2(x+3)2+2y=2\left(x+3\right)^2+2y=2(x+3)2+2
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y=(x+3)2−2y=\left(x+3\right)^2-2y=(x+3)2−2
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y=(x−3)2−2y=\left(x-3\right)^2-2y=(x−3)2−2
Analyze the graph and determine its standard form
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y=3(x2)+2y=3\left(x^2\right)+2y=3(x2)+2
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y=(x−3)2+2y=\left(x-3\right)^2+2y=(x−3)2+2
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y=2(x+3)2+2y=2\left(x+3\right)^2+2y=2(x+3)2+2
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y=(x+3)2−2y=\left(x+3\right)^2-2y=(x+3)2−2
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y=(x−3)2−2y=\left(x-3\right)^2-2y=(x−3)2−2
Where is the focus of this parabola?
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F(-2,-2)
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F(-2,-3)
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F(3,2)
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F(3, 1.75)
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F(3, 2.25)
Where is the directrix of this parabola?
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y = -2
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y= -3
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y= 2
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y= 1.75
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y = 2.25
Where is the axis of symmeetry of this parabola?
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x = -2
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x= -3
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x= 2
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y= -3
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y = 2
What is the difference between this two parabolas?
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The h coordinate
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The k coordinate
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The Vertex
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The axis of symmetry
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The a coefficient
Where is the center of the following parabola? x=14(y+2)2−10x=\frac{1}{4}\left(y+2\right)^2-10x=41(y+2)2−10
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(2,-10)
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(-2,-10)
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(1/4, 10)
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(-10,-2)
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(-10,2)
Where is the focus of this parabola found with respect to its center? x=14(y+2)2−10x=\frac{1}{4}\left(y+2\right)^2-10x=41(y+2)2−10
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to the left
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to the right
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above it
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below it
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it can´t be determined
To what direction does this parabola open? x=14(y+2)2−10x=\frac{1}{4}\left(y+2\right)^2-10x=41(y+2)2−10
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to the left
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to the right
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above it
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below it
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it can´t be determined
Which equation would give the graph of a parabola?
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y = 2x - 3
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y = x2 + 1
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y = x2 + 4
Is the following parabola concave up or concave down?
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Concave down
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Concave up
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Neither
How can you tell whether a parabola is facing up or facing down by looking at the equation?
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The vertex tells you the direction of the opening
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The value of "a" tells you the direction of the opening.
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All parabolas open upward
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All parabolas open downward
If the a value is positive in the equation of y = ax2 + c, which direction does the graph open?
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up
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down
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left
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right
If the a value is negative in the equation y = ax2 + c , which direction does the parabola open?
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up
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down
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left
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right
The X axis goes...
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Horizontally, or across
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Vertically, or up and down
The Y axis goes...
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Vertically, or up and down
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Horizontally, or across
Which letter in a equations y = ax2 + c represents the y-intercept?
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a
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b
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c
What is the y-intercept of the parabola y = 5x2 - 3
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5
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3
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- 3
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-5
What is the y-intercept of the parabola?
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-4
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4
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-3
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0
What is the equation of this graph?
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y = x2 + 1
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y = - x2 + 1
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y = x2
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y = - x2
What is the equation of the following graph?
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y = 2x2
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y = x2 + 2
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y = x2 - 2
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y = - 2x2
Which equation will result in the parabola being a narrower graph?
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y = 2x2 + 1
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y = 7x2 - 1
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y = 0.5x2 + 1
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y = x2
The equation of the parabola is:
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y = x + 2
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y = x2 + 2
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y = x - 2
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y = x2 - 2
What is the equation of this graph?
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y = - x2
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y = - x2 - 3
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y = - x2 + 3
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y = x2 + 3
Which equation would result in the parabola being wider?
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y = 0.5x2 + 2
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y = x2
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y = 10x2 + 7
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y = - 3x2 - 2
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