Given the vertex and directrix, learn to write the standard form of a parabola

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Mathematics
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11th Grade - University
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Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in writing the standard form of a parabola's equation?
Identify the axis of symmetry
Graph the parabola
Calculate the distance to the focus
Determine the parabola's orientation
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the focus of a parabola related to the vertex and directrix?
It is the same distance from the vertex as the directrix but in the opposite direction
It is twice the distance from the vertex to the directrix
It is equidistant from the vertex and the directrix
It is always below the directrix
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of P if the distance from the vertex to the directrix is 5?
P = -5
P = 0
P = 5
P = 10
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which form does the equation of a parabola with a vertical axis of symmetry take?
Y - K = 4P(X - H)^2
X - H = 4P(Y - K)^2
X - H^2 = 4P(Y - K)
Y - K^2 = 4P(X - H)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What values are substituted for H and K in the equation X - H^2 = 4P(Y - K)?
H = 0, K = 0
H = 1, K = 8
H = 8, K = 1
H = 5, K = 5
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final simplified form of the equation after expanding and distributing?
Y = 20X^2 - 2X + 161
Y = 1/10 X^2 - 1/20 X + 161/10
Y = 1/20 X^2 - 1/10 X + 161/20
Y = X^2 - 2X + 161
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to reduce the equation to its simplest form?
To make it easier to solve for X
To verify the accuracy of calculations
To ensure it fits the standard form
To make it easier to graph
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