Do Now. Sketch and discuss the parabola
y² + 3x = 0
y
Focus:
10
9
8
Directrix:
7
6
5
4
Length of LR:
Endpoints of LR:
3
2
1
0
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
1
2
3
4
5
6
7
8
9 10
x
5.2 (day 2) Notes
Ex 1: Find an equation of the parabola(s)
with vertex at the origin and focus (-4, 0).
y
10
9
8
7
6
5
4
3
2
1
0
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
1
2
3
4
5
6
7
8
9 10
x
Ex 2: Find the equation of the parabola with vertex at
the origin and directrix y - 7 = 0.
y
10
9
8
7
6
5
4
3
2
1
0
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
1
2
3
4
5
6
7
8
9 10
x
Ex 3: Find the equation of the parabola with vertex at
the origin, length of the latus rectum is 10, and
opens downward.
y
10
9
8
7
6
5
4
3
2
1
0
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
1
2
3
4
5
6
7
8
9 10
x
Ex 4: Find the equation of the parabola with vertex
at the origin, axis is the x-axis, and goes through
the point (3, -4).
y
10
9
8
7
6
5
4
3
2
1
0
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
1
2
3
4
5
6
7
8
9 10
x