10.2 the parabola. a parabola is defined as the locus of all points in a given plane that are the...
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10.2The Parabola
A parabola is defined as the locus of all points in a given plane that are the same distance from a fixed point, called the focus, and a given line, called the directrix.
111 QPFP
Directrix
focus
222 QPFP 333 QPFP
Parabola with Axis of Symmetry Parallel to y-Axis, Opens up, a > 0.
V = (h, k)
y
x
Axis of symmetry x = h
a
a
kyahx 42
Parabola with Axis of Symmetry Parallel to y-Axis, Opens down, a < 0.
y
x
V = (h, k)
Axis of symmetry x = h
a
a
kyahx 42
Parabola with Axis of Symmetry Parallel to x-Axis, Opens to the Right, a > 0.
V = (h, k)
y
x
Axis of symmetry
y = k
a
a
hxaky 42
Parabola with Axis of Symmetry Parallel to x-Axis, Opens to the Left, a< 0.
Axis of symmetry y = k
y
x
V = (h, k)
a a
hxaky 42
Even if you graph the vertex, the axis of symmetry, the focus and the directrix, the shape of the parabola is still in question.
That is where the latus rectum comes in. The latus rectum is a segment that goes through the focus, perpendicular to the axis of symmetry. The endpoints are points on the parabola and they help to define the shape.
parabola notes
28)3( 2 yx
1162 2 xy
The general form of the equation of a parabola
2 0y Dx Ey F
2 0x Dx Ey F If x is the squared term.
If y is the squared term.
Write the equation in standard form, list the coordinates of the vertex, the focus, and the equation of the directrix line. Then graph the parabola.
2 4 8 20 0x x y
2 8 8 8 0y y x
Write the equation in standard form, list the coordinates of the vertex, the focus, and the equation of the directrix line. Then graph the parabola.
1) Sketch!2)Does the parabola open
up, down, right or left?3) Is x or y the squared term?4) a = _____5) 4a = ______6)should 4a be
positive or negative?
Write the equation of the parabola in standard form.
1) Sketch!2)Does the parabola open
up, down, right or left?3) Is x or y the squared term?4) a = _____5) 4a = ______6)should 4a be
positive or negative?
Write the equation of the parabola in standard form.
focus (3,5); directrix x = 5
1) Sketch!2)Does the parabola open
up, down, right or left?3) Is x or y the squared term?4) a = _____5) 4a = ______6)Should 4a be
positive or negative?
Write the equation of the parabola in standard form.
vertex (5,1); directrix x = -1
Write the equation of the parabola in standard form.
1) Decide whether the x or the y is the squared term.
2) Find the coordinates of the vertex.
3) Find p
4) Calculate 4p. Should it be positive or negative?
Write the equation of the parabola in standard form.
1) Decide whether the x or the y is the squared term.
2) Find the coordinates of the vertex.
3) Find p
4) Calculate 4p. Should it be positive or negative?