10.2 Parabolas What you should learn: Goal1 Goal2 Graph and write equations of parabolas. Identify...
17
10.2 Parabolas What you should learn: Goal Goal 1 1 Goal Goal 2 2 Graph and write equations of parabolas. Identify the FOCUS and DIRECTRIX of the parabola. 10.2 Parabolas 10.2 Parabolas Goal Goal 3 3 Write the Standard form of the equation of the parabola.
-
Upload
charleen-bishop -
Category
Documents
-
view
212 -
download
0
Transcript of 10.2 Parabolas What you should learn: Goal1 Goal2 Graph and write equations of parabolas. Identify...
10.2 Parabolas
What you should learn:GoalGoal 11
GoalGoal 22
Graph and write equations of parabolas.
Identify the FOCUS and DIRECTRIX of the parabola.
10.2 Parabolas10.2 Parabolas
GoalGoal 33 Write the Standard form of the equation of the parabola.
ParabolasParabolasWe already know the graph of We already know the graph of y y = a= axx22
is a parabola with vertex (0,0) and is a parabola with vertex (0,0) and AOS AOS x x = 0= 0
Every parabola has the property that Every parabola has the property that any point on it is equidistant from a any point on it is equidistant from a point called the point called the FocusFocus and a line and a line called the called the directrixdirectrix..
10.2 Parabolas10.2 Parabolas
FocusLies on AOS
Directrix
10.2 Parabolas10.2 Parabolas
The Focus is a point.The Focus is a point.The Directrix is a lineThe Directrix is a line
(the vertex is ½ way between the (the vertex is ½ way between the focus and directrix)focus and directrix)
y = ay = axx2 2 standard equation beforestandard equation beforea =4pa =4pxx22 = 4p = 4pyy new equation. new equation.
10.2 Parabolas10.2 Parabolas
x2=4py, p>0
Focus (0,p)
Directrixy=-p
10.2 Parabolas10.2 Parabolas
x2=4py, p<0
Focus (0,p)
Directrixy=-p
10.2 Parabolas10.2 Parabolas
y2=4px, p>0
Directrixx=-p
Focus (p,0)
10.2 Parabolas10.2 Parabolas
y2=4px, p<0
Focus (p,0)
Directrixx=-p
10.2 Parabolas10.2 Parabolas
Standard equation of Parabola (vertex @ origin)
Equation Focus Directrix AOS
x2=4py (0,p) y = -pVertical
(x=0)
y2=4px (p,0) x = -pHorizontal
(y=0)
10.2 Parabolas10.2 Parabolas
Identify the Focus and Directrix of the parabola
x = -1/6y2
• Since y is squared, AOS is horizontal• Isolate the y2 → y2 = -6x• Since 4p = -6• p = -6/4 = -3/2
• Focus : (-3/2,0) Directrix : x=-p=3/2• To draw: make a table of values & plot • p<0 so opens left so only choose neg values for x
10.2 Parabolas10.2 Parabolas
GoalGoal 22
10.2 Parabolas10.2 Parabolas
Your Turn!
• Find the focus and directrix, then graph
x = 3/4y2
• y2 so AOS is Horizontal
• Isolate y2 → y2 = 4/3 x
• 4p = 4/3 p = 1/3
• Focus (1/3,0) Directrix x=-p=-1/3
10.2 Parabolas10.2 Parabolas
10.2 Parabolas10.2 Parabolas
Writing the equation of a parabola.
• The graph shows V=(0,0)
• Directrex y=-p=-2
• So substitute 2 for p
10.2 Parabolas10.2 Parabolas
GoalGoal 33
• x2 = 4py
• x2 = 4(2)y
• x2 = 8y
• y = 1/8 x2 and check in your calculator
10.2 Parabolas10.2 Parabolas
Your turn!
• Focus = (0,-3)
• X2 = 4py
• X2 = 4(-3)y
• X2 = -12y
• y=-1/12x2 to check
10.2 Parabolas10.2 Parabolas
Assignment
10.2 Parabolas10.2 Parabolas
