Transcript Document

OCF.01.4 - Finding Max/Min Values of
Quadratic Functions
MCR3U - Santowski
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(A) Review - Max/Min Values
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Recall that a parabola has a maximum if the
parabola opens downward, which can be identified
from an equation if the value of a is negative.
Recall that a parabola has a minimum value if the
parabola opens upward, which can be identified
from an equation if the value of a is positive.
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(B) Review - Max/Min Values and Forms of Quadratic
Equations
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Recall the various ways of using an equation to determine the
location of the vertex:
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(1) Vertex form: y = a(x - h)² + k
 the vertex at (h,k)
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(2) Intercept form: y = a(x - s)(x - t)
 the axis of symmetry is halfway between s and t
 when the x value for the is substituted into the equation, you
can find the coordinates of the vertex
(3) Standard form: y = ax² + bx + c
 axes of symmetry is at x = -b/(2a)
 when the x value for the is substituted into the equation, you
can find the coordinates of the vertex
(3) Standard Form: y = ax² + bx + c
 convert to vertex form using the method of competing the
square
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(C) Examples of Algebraic Problems
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(i) Find the max (or min) value of y = -0.5x2 - 3x + 1
(ii) Find the max (or min) point of y = 1/10x2 – 5x + ¼
(iii) Find the vertex of y = 3x2 – 4x + 6
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(D) Examples of Word Problems
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ex 1. A ball is thrown vertically upward from a balcony of an
apartment building. The ball falls to the ground. Its height, h
in meters above the ground after t seconds is given by the
equation h = -5t2 + 15t + 45.
(i) Determine the maximum height of the ball
(ii) How long does the ball take to reach the maximum
height?
(iii) How high is the balcony?
ex 2. Last year, talent show tickets are sold for $11 each and
400 people attended. It has been determined that a ticket
price rise of $1 causes a decrease in attendance of 20 people.
What ticket price would maximize revenue?
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(D) Examples of Word Problems
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ex 3. If you plant 100 pear trees in an acre, then the annual
revenue is $90 per tree. If more trees are planted, they
generate fewer pears per tree and the annual revenue per
tree is decreased by $0.70 for each additional tree planted.
Additionally, it costs $7.40 per tree per year for maintaining
each tree. How many pear trees should be planted to
maximize profit?
(i) What is the equation for revenue?
(ii) What is the equation for profit?
(iii) find the max value for the profit equation
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(E) Homework
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Nelson text, p314 - 316
Q1ac, 5ac, 6,7,8,12,15,16
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