Presentation on theme: "Conics. Parabolas Definition - a parabola is the set of all points equal distance from a point (called the focus) and a line (called the directrix). Parabolas."— Presentation transcript:
Parabolas Definition - a parabola is the set of all points equal distance from a point (called the focus) and a line (called the directrix). Parabolas are shaped like a U or C
Parabolas Equations - y = a(x - h) 2 + k –opens up if a > 0, opens down if a < 0. x = a(y - k) 2 + h –opens right if a > 0, opens left if a < 0.
Parabolas y = a(x - h) 2 + k x = a(y - k) 2 + h Vertex - the bottom of the curve that makes up a parabola. Represented by the point (h, k).
Parabolas Given the following equations for a parabola, give the direction of opening and the vertex. y = (x - 6) 2 - 4 opens up vertex is at (6, -4)
Parabolas x = (y + 5) 2 + 4 opens right. vertex = (4, -5) y = -5(x + 2) 2 opens down vertex = (-2, 0)
Parabolas x = -y 2 - 1 opens left vertex = (-1, 0)
Parabolas How are we going to graph these? Calculator of course!!! We will be using the conics menu (#9). Typing it will be KEY!!!!!
Parabolas Notice that you have four choices for parabolas. Two for x = and two for the y = types. How would we graph y = (x - 6) 2 - 4?
Parabolas y = (x - 6) 2 - 4 Which form would we use? The third one. A = 1 H = 6 K = -4
Parabolas y = (x - 6) 2 - 4 We already know that the vertex is at (6, -4), but the calculator will tell us if we hit G-Solv and then VTX (F5, then F4).
Parabolas Steps to graph a parabola (cause you gotta put in on graph paper for me to see). 1) choose the general equation that you will be working with.
Parabolas 2) Enter your variables. 3) Draw (F6) 4) Find the vertex (G-solve, then VRX => F5 then F4). 5) Plot the vertex on your graph paper.
Parabolas Now we need to plot a point on each side of the vertex. 6) if it is a y = equation, use the x value of the vertex as your reference. Plug in a value larger and smaller into the equation to get your y.
Parabolas 6) if it is a x = equation, use the y value of the vertex as your reference. Plug in a value larger and smaller into the equation to get your x. 7) Plot these two points on your graph paper.
Parabolas 8) connect your three points in a C or U shape. You’re done!!!
Parabolas Let’s try to graph some together. x = (y + 5) 2 + 4 y = -5(x + 2) 2 x = -y 2 - 1
Circles Definition: the set of all points that are equidistant from a given point (the center). The distance between the center and any point is called the radius.
Circles Equation - (x - h) 2 + (y - k) 2 = r 2 the center is at (h, k) the radius is r (notice that in the equation r is squared)
Circles Give the center and the radius of each equation. (x - 1) 2 + (y + 3) 2 = 9 center = (1, -3) radius = 3