The new and improved way to learn Quadratics
What to be prepared for
Standard Form Quadratic
y = a(x - h)2 + k what does this mean?
- If a < 0, the quadratic will open downwards.
- If a > 0, the quadratic will open upwards
If you increase the a value the arms will grow larger.
The (h,k) will always be the coordinates of the minimum and maximum values
The list on what to do.
New Topic Vertex form
The Parabola is what happens to the graphing a Quadratic Relation- containing very important segments that come together to create a Parabola:
Vertex which is where the parabola and the axis of symmetry meet: (x,y)
Axis of Symmetry which divides the parabola equally: (x=#)
X-Intercept is also known as (zeroes/all real numbers) is where the line passes through the x axis: (#,0)
Y-Intercept where the line passes through the y axis: (0,#)
Optimal Value is the Y coordinate of the Vertex and the Optimal Value is also the highest or lowest point: (y=#)
Converting From form to form
Converting vertex form to factored form
To convert from Vertex form to factored form
1. Change y as 0
2. Place k value over the equal sign
3. Divide "a" value form both sides of equation
4. Square root both sides so you can get rid of the square root on the right side
5. Finally move your "h" value over the equal sign
Converting Standard form to vertex form
1. Remove the common factor from the x^2 and the x term(coefficient)
2. Locate the constant that must be added and subtracted to create a perfect square. Rewrite the expressions by adding and subtracting the constant
3. group the three terms that form the perfect square ( move subtracted value outside the brackets by multiplying it by the common factor fist )
4.factor the perfect square and collect all like terms
Axis of Symentry
Word problem finding the answer
- The product of two consecutive negative integers is 1122. What are the numbers?
Remember that consecutive integers are one unit apart, so my numbers are n andn + 1. Multiplying to get the product, I get:
n(n + 1) = 1122
n2 + n = 1122
n2 + n – 1122 = 0
(n + 34)(n – 33) = 0 Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved
The solutions are n = –34 and n = 33. I need a negative value, so I'll ignore "n = 33" and
take n = –34. Then the other number is n + 1 = (–34) + 1 = –33.
The two numbers are –33 and –34.
Note that the second value could have been gotten by changing the sign on the extraneous solution. Warning: Many students get in the very bad habit of arbitrarily changing signs to get the answers they need, but this does not always work, and will very likely get them in trouble later on. Take the extra half a second to find the right answer the right way.
Cool things to know
Math in words
- There was a negative Boy, who was confused about whether or not he should go to a radical party. The Boy was square, so he missed out on 4 Awesome Chicks and he cried until the party was over at 2 Am.
Hint: x=[-b +/- sqrt(b^2-4ac)]/2a
A: Parabolas (pair of bolas)
A : Because they have sine and cosine to get a tan and don't need the sun!