Algebra 3 VIDEO NOTES Sec. 11.2 The Parabola
Parabola - __________________________________________________________________
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Equations of vertical and horizontal parabolas with the vertex (0, 0)
Vertex
(0, 0)
(0, 0)
(0, 0)
(0, 0)
Equation
x2 = 4ay
x2 = -4ay
y2 = 4ax
y2 = -4ax
Description
Axis of Symmetry is the y-axis,
Axis of Symmetry is the y-axis,
Axis of Symmetry is the x-axis,
Axis of Symmetry is the x-axis,
Opens Up
Opens Down
Opens Right
Opens Left
** a is the distance from the vertex to the focus and the vertex to the directrix **
*** Solve for a by setting the coefficient equal to 4a or -4a ***
****** DRAW A PICTURE ******
Analyze the equation means to find the vertex, focus, directrix, and graph.
Example 1. Analyze x2 = -8y
Example 2. Find the equation if the vertex is (0, 0) and the focus is (3,0)
Example 3. Find the equation if the vertex is (0,0) and the directrix is y = -5
Example 4. Find the equation if the vertex is (0, 0) and the graph contains the point (-1, -2).
Opens left.
Example 5. A searchlight is shaped like a paraboloid of revolution. If the light source is
located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how
deep should the opening be?
Equations of vertical and horizontal parabolas with the vertex (h, k)
Vertex
Equation
Description
2
(h, k)
(x – h) = 4a(y – k)
Opens Up
2
(h, k)
(x – h) = -4a(y – k)
Opens Down
2
(h, k)
(y – k) = 4a(x – h)
Opens Right
(h, k)
(y – k)2 = -4a(x – h)
Opens Left
** a is the distance from the vertex to the focus and the vertex to the directrix **
*** Solve for a by setting the coefficient equal to 4a or -4a ***
****** DRAW A PICTURE ******
Example 6. Find the equation with the vertex at (2, -3) and the focus at (5, -3).
Example 7. Find the equation from the vertex (-3, 1) and the point (9, -11). The parabola
opens down.
CLASSWORK: Pages 779 – 881 11-14, (Find Eq. only 20, 23, 26, 30, 34), 38, 39, 42, 46,
56, 58, 64, 70