```Quadratic Function
Find the axis of symmetry and vertices:
f(x) = 2x2 – 5x + 1
g(x) = x2 + 2√3x + 3
h(x) = -3x2 + 5x – 3
 How many real roots does each function
have?
 Can you factor the above equations?
 Many
times we can not factor the
does not have integers for roots, or
because it does not even have real
roots. In those cases, we use the
 The
a, b and c are from the standard
y = ax2 + bx + c
 The quadratic formula may be used to
factor any quadratic function. The roots
are:
 b  b  4ac
x
2a
2
 b  b  4ac
x
2a
2
 The
discriminant is the number under
the square root sign. The discriminant
is:
b  4ac
2
 The
discriminant determines how many
real roots the quadratic function has.
 b  b  4ac
x
2a
2
 What
1.
are the # & type of roots if:
If the discriminant is positive?
2 real roots
2.
If the discriminant is negative?
2 imaginary roots
3.
If the discriminant is zero?
1 real root duplicity 2
 b  b  4ac
x
2a
2
Let f(x) = 2x2 – 5x + 1
What is the value of the discriminant?
5  17
4
(5)2  4(2)(1)  25  8  17
How many and type of roots does f(x)
have?
2 real roots
Calculate the zeros of f(x) using the 5  17
4
 b  b  4ac
x
2a
2
Let g(x) = -3x2 + 5x – 3
What is the value of the discriminant?
2
5  4 3(3)  25  36  11
How many and type of roots does g(x)
have? 2 imaginary roots
5  17
4
Calculate the zeros of g(x) using the
5 i 11

6
6
Geometry
 The
seats in a theater are arranged in
parallel rows that form a rectangular
region. The number of seat in each row
of the theater is 16 fewer than the
number of rows. How many seats are
in each row of a 1161 seat theater?
Accounting
 To
approximate the profit per day for
her business, Mrs. Howe uses the
formula p = - x2 + 50x – 350. The profit,
p, depends on the number of cases, x,
of decorator napkins that are sold.
 How many cases of napkins must she
sell to break even?
 How many cases should she sell to
maximize profit?
 Find the maximum profit.
Practice
 Page
93, # 3 – 21 by 3’s and 22 – 25 all
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