Quadratic FunctionFind the axis of symmetry and vertices:

f(x) = 2x2 – 5x + 1

g(x) = x2 + 2√3x + 3

h(x) = -3x2 + 5x – 3How many real roots does each

function have?Can you factor the above equations?

Quadratic FunctionMany 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 FormulaThe a, b and c are from the standard

form of the quadratic equation:

y = ax2 + bx + cThe quadratic formula may be used to

factor any quadratic function. The roots are:

a

acbbx

2

42

The discriminant is the number under the square root sign. The discriminant is:

The discriminant determines how many real roots the quadratic function has.

Quadratic Formula

a

acbbx

2

42

acb 42

What are the # & type of roots if:

1. If the discriminant is positive?

2. If the discriminant is negative?

3. If the discriminant is zero?

Quadratic Formula

a

acbbx

2

42

2 real roots

2 imaginary roots

1 real root duplicity 2

Let f(x) = 2x2 – 5x + 1

What is the value of the discriminant?

How many and type of roots does f(x) have?

Calculate the zeros of f(x) using the quadratic equation:

Quadratic Formula

a

acbbx

2

42

4

175

4

175

17825)1)(2(4)5( 2

2 real roots

Let g(x) = -3x2 + 5x – 3

What is the value of the discriminant?

How many and type of roots does g(x) have?

Calculate the zeros of g(x) using the quadratic equation:

Quadratic Formula

a

acbbx

2

42

4

175

2 imaginary roots

6

11

6

5 i

113625)3(3452

GeometryThe 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?

AccountingTo 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.

PracticePage 93, # 3 – 21 by 3’s and 22 – 25 all