The document provides instruction on solving quadratic equations using the quadratic formula. It introduces the quadratic formula as the ultimate method for solving all quadratic equations, including those deemed previously "unsolvable". The formula is presented as ax^2 + bx + c = 0, and students are walked through examples of plugging values into the formula and solving for x. While the quadratic formula can solve all quadratic equations, it requires memorizing the formula and being careful with signs and order of operations.

1. SOLVING QUADRATIC EQUATIONS
USING THE QUADRATIC FORMULA
April 15, 2014

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

3. 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

4. **She’s beautiful, and she’s all yours
The Quadratic Formula:

5. 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

6. 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

7. EXAMPLE 1
x = 5 + 7
4
x = 12
4
x = 5 - 7
4
x = -2
4
x = 3
x = -1/2

8. 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

9. 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

10. x = -7 ± 11
4
x = 4
4
x = 1
x = -9/2
EXAMPLE 2
x = -7 - 11
4
x = -18
4
x = -7 + 11
4

11. x = -(1) ± √(1)2 – 4(1)(-1)
2(1)
LAST EXAMPLE
Solve x2 + x – 1 = 0
First we need to identify a, b & c

12. PROBLEM 3
x = -(1) ± √(1)2 – 4(1)(-1)
2(1)
We can go no further since 5
can’t be squared.
x = -1 + √5
2
x = -1 - √5
2
LAST EXAMPLE
x = -1 ± √5
2
x = -1 ± √1+ 4
2

13. COMPLETE & SUBMIT CLASS
WORK TODAY!