Unit 7 Conics Study Guide
Targets
Name: ________________________ Per: ______
Internet Resources/Notes/Questions
Hint: Khan Academy has a good
video for this one—Don’t get
excited. Just this one, OK?.
Sample Question
Find the equation for a parabola
given the focus and directrix.
(Or focus (or directrix) and the
vertex
Find the equation for a parabola
given the focus and a point.
Find the focus and directrix
given the equation of a parabola.
Accurately graph a quadratic
equation in a different form.
Identify the function of different
elements of different forms of a
quadratic equation.
Graph (and know all of the
above) for a graph that opens
left/right.
Find the equation of the parabola with focus (2,
6) and directrix y = –8.
Find the equation of the parabola given F (1, –1)
and P1 (3, –1),
Given the equation y = 4x2 + 8x +36, find the
vertex, focus, and directrix.
Graph the equation (x – 4)2 = ½ (y – 5).
Given the equation (x – h)2 = 4r (y – k), identify
the role of each of the elements.
Find the equation for the parabola given the
focus (0, 3) and the directrix x = 4.
Vocabulary
Parabola: _________________________________________________________________________________________
Vertex: ___________________________________________________________________________________________
Focus: ___________________________________________________________________________________________
Directrix: _________________________________________________________________________________________
Line of Symmetry: __________________________________________________________________________________
Geometric Form: ___________________________________________________________________________________
Label the following elements on the graph and describe as follows using the example. Draw arrows to each.
y
10
Focus: _________________________
Directrix: _______________________
5
Distance from Focus to Vertex (r): ____
Equation of the parabola with focus (6, 6)
& the point (3, 10) (Yikes, sideways!)
#1. Distance between (6, 6) & (3, 10) = 5
0
x
-5
Vertex: _____________________
#2. Directrix: x = –2
Point1: _________ Point2: _________
Distance from point1 to the focus
and point1 to directrix: __________
-10
-10
-5
0
5
10
Horizontal Distance from focus to
Point2: ________ What other point has the same distance to the
parabola? _____________
#3. Line of Symmetry y = 6. Therefore,
Vertex ( 2, 6) (Midway between –2 & 6)
#4. x = ___(y – 6)2 + 2
#5. 3 = a(10 – 6)2 + 2
3 = 16a + 2
1 = 16a
a = 1/16
How does the horizontal distance from the focus the parabola compare
#6. x = 1/16(y – 6)2 + 2
to the distance from the focus the vertex? ________________________
How can you tell if a parabola will open up or down given the Focus and Directrix?
How can you tell if a parabola will open left or right given the Focus and Directrix?
Find the equation for a parabola given the focus and a point.
Regardless of the orientation of a parabola, any point on a parabola is equidistant to the focus and to the ______________.
1.
Find the distance between the focus and the ____________.
2.
The distance from the point to the directrix must be equal to the distance from the
point to the _________ (#1 above). This point on the directrix would have an x value (or
y-value if horizontal) the _________ as the point on the parabola. This distance is the
length of the difference of the y-values (or x-values if horizontal).
3.
The vertex and the focus of the parabola both lie on the Line (Axis) of
____________ and the vertex lies half-way _____________ the focus and the directrix.
4.
Write the equation in __________ form (y = a(x – h)2 + k.) — or inverse if
horizontal.
5.
Plug in the given point to solve for _____.
6. Insert a into your equation in the form you need.
Note: to find a, if you know that a = 1/4r where r (also commonly labeled “q”) is the distance from the vertex to the
_________ or directrix, you can use that whether the parabola is vertical or horizontal.
Find the equation for a parabola given the focus and directrix.
1. Find the vertex between the focus and directrix.
2. Put the vertex into the vertex form of a quadratic ______________.
3. Find a by the equation a = (where r—or q — is the distance
between the focus and the vertex).
4. Rewrite the _____________ with the new a value.
5. Simplify if necessary.
Example: Find the equation of the parabola
with focus (2, 6) and directrix y = –8.
#1. Vertex: (2, –1)
#2. y = a (x – 2)2 – 1
#3. a =
∙
#4. y =
(x – 2)2 – 1
Find the equation for a parabola given the focus (or directrix) and the vertex.
Follow the steps above from #2.
Determine whether a parabola will open up/down or left/right.
1. If a in the equation is positive, the parabola will open ________ or right.
2. If the x is squared in the equation, the parabola will open up or ____________.
3. If the y is squared in the equation, the parabola will open __________ or right.
Write out and list the advantages of the following forms of quadratic equations including
Standard Form: _____________________________________________________________________________
Factored Form: _____________________________________________________________________________
Vertex Form: _______________________________________________________________________________
Geometric Form: ____________________________________________________________________________