Topics
>
Precalculus>
Conic Sections>
Graph Parabolas Given the Vertex, Focus and Directrix>
Graph Parabolas Given the Vertex, Focus and Directrix 1Graph Parabolas Given the Vertex, Focus and Directrix 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
 1
 2
 3
 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
 1
 2
 3
 4
 Answered
 Review

Question 1 of 4
1. Question
Write the equation of the parabola given the following:Focus `(0,3)`Vertex `(0,0)` `x^2=` (12)`y`
Hint
Help VideoCorrect
Correct!
Incorrect
Standard Form (Concave Up)
`x^2=4``a``y`Focus
`(0,``a``)`Standard Form (Concave Down)
`x^2=4``a``y`Focus
`(0,``a``)`First, plot the given focus and vertexFocus`(0,3)`Vertex`(0,0)`Based on the diagram, the focal length, `a`, is equal to `3`Now that we know `a`, we can also plot the directrix.`y` `=` ```a` Directrix Formula `y` `=` ```3` Next, draw the parabola. Remember that the parabola’s concavity should be opposite the directrixSince the parabola is concave up, use `x^2=4``a``y`Finally, form the equation by substituting `a=3` to the chosen standard form`x^2` `=` `4``a``y` Standard Form `x^2` `=` `4``(3)``y` Substitute `a=3` `x^2` `=` `12y` `x^2=12y` 
Question 2 of 4
2. Question
Write the equation of the parabola given the following:Focus `(0,1)`Vertex `(0,0)` `x^2=` (4)`y`
Hint
Help VideoCorrect
Great Work!
Incorrect
Standard Form (Concave Up)
`x^2=4``a``y`Focus
`(0,``a``)`Standard Form (Concave Down)
`x^2=4``a``y`Focus
`(0,``a``)`First, plot the given focus and vertexFocus`(0,1)`Vertex`(0,0)`Based on the diagram, the focal length, `a`, is equal to `1`Now that we know `a`, we can also plot the directrix.`y` `=` `a` Directrix Formula `y` `=` `1` Next, draw the parabola. Remember that the parabola’s concavity should be opposite the directrixSince the parabola is concave down, use `x^2=4``a``y`Finally, form the equation by substituting `a=1` to the chosen standard form`x^2` `=` `4``a``y` Standard Form `x^2` `=` `4``(1)``y` Substitute `a=1` `x^2` `=` `4y` `x^2=4y` 
Question 3 of 4
3. Question
Write the equation of the parabola given the following:Directrix `x=1/4`Vertex `(0,0)` `y^2=` (x)
Hint
Help VideoCorrect
Excellent!
Incorrect
Standard Form (Concave Right)
`y^2=4``a``x`Focus
`(``a``,0)`Standard Form (Concave Left)
`y^2=4``a``x`Focus
`(``a``,0)`First, plot the given directrix and vertexDirectrix `x=1/4`Vertex`(0,0)`Based on the diagram, the focal length, `a`, is equal to `1/4`Now that we know `a`, we can also plot the focus.`(``a``,0)` becomes `(``1/4``,0)`Next, draw the parabola. Remember that the parabola’s concavity should be opposite the directrixSince the parabola is concave right, use `y^2=4``a``x`Finally, form the equation by substituting `a=1/4` to the chosen standard form`y^2` `=` `4``a``x` Standard Form `y^2` `=` `4``(1/4)``x` Substitute `a=1/4` `y^2` `=` `x` `y^2=x` 
Question 4 of 4
4. Question
Write the equation of the parabola given the following:Directrix `x=2`Vertex `(0,0)` `y^2=` (8)`x`
Hint
Help VideoCorrect
Correct!
Incorrect
Standard Form (Concave Right)
`y^2=4``a``x`Focus
`(``a``,0)`Standard Form (Concave Left)
`y^2=4``a``x`Focus
`(``a``,0)`First, plot the given directrix and vertexDirectrix `x=2`Vertex`(0,0)`Based on the diagram, the focal length, `a`, is equal to `2`Now that we know `a`, we can also plot the focus.`(``a``,0)` becomes `(``2``,0)`Next, draw the parabola. Remember that the parabola’s concavity should be opposite the directrixSince the parabola is concave left, use `y^2=4``a``x`Finally, form the equation by substituting `a=2` to the chosen standard form`y^2` `=` `4``a``x` Standard Form `y^2` `=` `4``(2)``x` Substitute `a=2` `y^2` `=` `8x` `y^2=8x`
Quizzes
 Write an Equation for Circle Graphs
 Graph Circles in Standard Form
 Graph Circles in Expanded Form
 Graph Parabolas (Focus and Directrix) 1
 Graph Parabolas (Focus and Directrix) 2
 Graph Parabolas Given the Vertex, Focus and Directrix 1
 Graph Parabolas Given the Vertex, Focus and Directrix 2
 Graph Hyperbolas
 Write an Equation for Hyperbolas
 Graph Cubic Curves
 Write an Equation for Cubic Curves
 The Exponential Curve