Download PreCalculus Fall 2014 Lesson 022 _Vertex Equation of a parabola

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Lesson Plan #022
Class: PreCalculus
Date: Monday October 27th, 2014
Topic: Vertex equation of a parabola
Aim: How do we use the vertex equation of a parabola?
Objectives:
1) Students will be able to use the vertex equation of a parabola.
HW# 022: Page 142 #’s 1, 4 8, 24, 36, 42, 50, 66, 82, 94
Do Now:
A baseball (.145 kg and .074m in diameter) is hit at a point 3 feet above the ground at a velocity of 100 feet per second (30.48m/s)
and at an angle of 45o with respect to the ground.
The path of the baseball is given by the function
baseball (in feet) and
f ( x)  0.0032 x 2  x  3 where f (x) is the height of the
x is the horizontal distance from the plate (in feet).
a) What is the maximum height reached by the baseball? (Hint: the graph of the function is a parabola that faces down.
The maximum height is reached at the axis of symmetry)
b) How far does the baseball travel horizontally? (The distance the graph travels horizontally will occur when the
object lands on the GROUND)
c) Graph the equation in your graphing calculator. For the window use x-min = 0, x-max = 400, xscl = 20, y-min=-20,
ymax=100, y-scl=20.
Procedure:
Write the AIM and DO NOW
Get students working!
Take attendance
Give back work
Go over HW
Collect HW
Let’s go to http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html to
take a look at a parabolic path.
Let’s go to this site http://www.mathopenref.com/quadraticexplorer.html to explore the format of a quadratic function.
What is a parabola?
Let’s go to
http://www2.seminolestate.edu/lvosbury/CalculusII_Folder/ConicSections.htm
http://www.intmath.com/plane-analytic-geometry/4-parabola.php
http://calculus7.com/sitebuildercontent/sitebuilderfiles/outgoing.avi
Derive vertex form of the equation of a parabola with vertex at the origin.
parabola whose axis
f ( x)  a( x  h)2  k , a  0 is in vertex form. The graph of f is a
of symmetry is the vertical line x  h and whose vertex is the point ( h, k ) . If a  0 , the parabola opens upward, and if
a  0, the parabola opens downward.
The quadratic function given by
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Assignment #1:
Sketch the graph of each quadratic function by hand. Identify the vertex and any
A)
f ( x)  ( x  5)  6
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B)
Assignment #2:
Find the vertex form of the equation of each parabola
A)
x intercepts.
h( x)  3x 2  6 x  5
B)
Assignment #3:
Find the quadratic function that has the given vertex and whose graph passes through the given point
A) Vertex (3,4) Point (1,2)
Assignment #4:
B) Vertex (2,3)
Point (0,2)
C) Vertex (-2,2) Point (-1,0)
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Assignment #5:
Assignment #6:
Assignment #7: