April 15, 2014

SOLVING QUADRATIC EQUATIONS

USING THE QUADRATIC FORMULA

April 15, 2014

# 27. Change equation to the one on the board.

You now possess 5 methods to solve quadratic equations. They are:

C) Finding square roots

B) Completing the square

D) Creating a table of x/y values

A) Factoring

And thus, it is time. You have proven yourself and are ready for the awesome responsibility awaiting you..

You are about to acquire the ultimate weapon in your battle to slay the quadratic dragon.

Ladies & Gentlemen, the nuclear option, the peace maker, the final solution...

Beware though, it is wild and not easily tamed.

E) Graphing

**She’s beautiful, and she’s all yours

The Quadratic Formula:

THE QUADRATIC FORMULA

.....Solves every quadratic equation, making ‘unsolvable’ a thing of the past.

Imaginary numbers are not covered until Algebra 2. This means that we still may have some equations that are unsolvable to us.

Pro’s Cons

No figuring out what method to use

Formula must be memorized

If used every time, solving will be easier and faster

Must always be aware of signs and order of operations

Solve the equation with the Quadratic Formula

2x2 – 5x – 3 = 0

The first thing we need to do is to see if this fits the first formula.

It does since it has the variable squared, the coefficient and the constant all equaling to zero.

Next we find the a, b & c and put them into the second formula. a = 2 b = -5 c = -3

EXAMPLE 1

x = 5 + 7

4

x = 12

4

x = 5 - 7

4

x = -2

4

x = 3

x = -1/2

Rearrange to standard form first

EXAMPLE 2

Solve 2x2 + 7x = 9

2x2 + 7x – 9 = 0

Identify the a, b & c and plug them in.

2x2 + 7x – 9 = 0

Now we identify the a, b & c and

place it in formula two. Then we

solve.

x = -(7) ± √(7)2 – 4(2)(-9)

2(2)

x = -7 ± √49 – (- 72)

4

x = -7 ± √121

4

x = -7 ± 11

4

EXAMPLE 2

x = -7 ± 11

4

x = 44

x = 1x = -9/2

EXAMPLE 2

x = -7 - 114

x = -184

x = -7 + 114

x = -(1) ± √(1)2 – 4(1)(-1)

2(1)

LAST EXAMPLE

Solve x2 + x – 1 = 0

First we need to identify a, b & c

PROBLEM 3

x = -(1) ± √(1)2 – 4(1)(-1)

2(1)

We can go no further since 5 can’t be squared.

x = -1 + √52

x = -1 - √52

LAST EXAMPLE

x = -1 ± √52

x = -1 ± √1+ 4

2

COMPLETE & SUBMIT CLASS WORK TODAY!