#### Quadratic Formula

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Quadratic Formula

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?
Quadratic Function
Many
times we can not factor the
quadratic function, either because it
does not have integers for roots, or
because it does not even have real
roots. In those cases, we use the
quadratic formula
Quadratic Formula
The
a, b and c are from the standard
form of the quadratic equation:
y = ax2 + bx + c
The quadratic formula may be used to
factor any quadratic function. The roots
are:
b b 4ac
x
2a
2
Quadratic Formula
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.
Quadratic Formula
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
Quadratic Formula
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
quadratic equation:
4
Quadratic Formula
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
quadratic equation:
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