This PowerPoint was adapted from http wwwpurplemathcommodulesquadform2htm and http teachershenricok12vausmathhcpsalgebra2Documents64200664ppt Looking Back In our previous lesson we solved quadratic function by ID: 267298
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Slide1
The Quadratic Formula with Mr. Ta
This PowerPoint
was adapted from
http://
www.purplemath.com/modules/quadform2.htm
and
http://
teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/6-4/2006_6_4.pptSlide2
Looking Back…
In our previous lesson, we solved quadratic function by completing the square
On your own, I would like for you guys to solve the following quadratic equation by completing the squarex
2
+ 6
x
– 7 = 0Now partner up with someone close to you and share answersPlease ask if anyone would like me to solve the problem on the boardSlide3
The
Quadratic FormulaWhen you solve the general formula using the technique, completing the square, you get the formula
I would like you guys to remember this formula on our upcoming test/quizhttps://
www.youtube.com/watch?v=z6hCu0EPs-o
(The Quadratic Formula Song)Slide4
Lets watch a demonstration…
https://www.youtube.com/watch?v=s80J2dAUUyISlide5
Some more practice problemsSlide6
Why is it important to use the Quadratic Formula?
The quadratic formula allows you to solve any quadratic equation, even if you cannot factor it.An important piece of the quadratic formula is what’s under the radical
:b
2
- 4ac
This piece is called the
discriminant
.Slide7
The Discriminant
In the general formula you can find the values for a, b, and c and plug it into the discriminant formula b
2
-
4ac
The three values types of values you can get from this formula is either a negative, positive, or zero value
Each value gives the function a different meaningAt your table of 4, discuss why the discriminant is important?
How does the discriminant correlate with graphs and parabolas?Slide8
Importance of Discriminants
The discriminants will tell you what your x-values will be and how many you will get.It can be seen as another form of checking your answer if your solution doesn’t match up to the definition of the discriminants.
Value
of the Discriminant
Nature of the Solutions
Negative
2 Imaginary SolutionsZero1 Real
Solution
Positive perfect square
2 Real Solutions –
Rational
Positive non-perfect square
2 Real Solutions – IrrationalSlide9
Discriminants and Graphs
Positive
Zero Value
Negative
This shows the correlation between the discriminant and the graphs of the quadratic formulas
As you can see, a positive value under the discriminant formula,
b
2
-
4ac
, will give you 2 x-intercepts
A zero under the formula will give you 1 x-intercept
And a negative value under the formula will give you 0 x-interceptSlide10
Work on the same problems, but this time, find the discriminant.
State whether it is positive, negative, or zero and state how many x-intercepts there are.