Download 5th hour Frogs Fleas and Painted Cubes

Blake Swisher
BrennanWells
Klaira Ekern
TriciaBeasley
Alexis Smith
Topics
Investigation 1: Introduction to Quadratic equations.-How to graph the
equations and also how when one side length gets shorter the other gets
longer.They have a fixed perimeter.
Investigation 2: Quadratic expressions-a quadratic expression is an
expression that is equal on both parts.
Investigation 3: Quadratic patterns of change-explore the patterns of change
for quadratic relationships.
Investigation 4: What is a quadratic function?-using mathmatical models to
describe and predict the effect of gravity on the position volocity, and
acceleration of falling and thrown objects.
Vocab
1.Constant term-a number in an algebraic expression that is not
multiplied by a variable.
2.Expanded form- the longest form of an equation.
3.Factored form- the short form of an equation.
4.Function- a relationship between two variables were the value of one
variable depends on the value of the other variable.
5. Like terms- terms with the same variable raised to the same
exponent.
6. Line of symmetry- A line that divides a graph or drawing into two
halves that are mirror images of eachother.
7. Maximum Value- the greatest possible line value of a Y function.
8. Minimum Value- The smallest Y value function.
9. Parabola- the graph of a quadratic equation.
10. Quadratic Term- A part of an algebraic
expression in which the variable is raised to the
second power.
11. Term- an expression with numbers and/or
variables multiplied together.
Things To Know
Parabola- The U-shape of a quadratic equated graph:
Vertex
Line of symmetry
Vertex- Maximum or minimum of a curve.
Line of symmetry- line that passed through the maximum or minimum point
of a parabola.
Function- A relationship between two variables.
SGx – S is for the starting value, G is for the growth factor, x is for the
unknown variable. This equation is for exponential growth.
Expanded form-Long form. Ex: x2+7x
Factored form- Short form. Ex: x(x+7)
Any equation containing x 2 is a quadratic equation, and can be graphed into
a quadratic graph. This graph would make a parabola, you could figure out
the x- intercepts, minimum or maximum point, or line of symmetry. Using
an equation to create a graph could be helpful
Example Problems
1. a. A square has a length of x centimeters. One dimension is increased by
2 centimeters. The other dimension is increased by 3 centimeters. Draw
the new rectangle.
2x
X2
6
3
x
x
x
b. Label the area of each of the 4 sections of the new rectangle.
c. Write 2 expressions for the area of the new rectangle, one in factored
form and one in expanded.
1. (x+2) (x+3)
2. x2+3x+2x+6
2. a. Make a table for the following equation. x(8-x)
Length
0
1
2
3
4
5
6
7
8
Area
0
7
12
15
16
15
12
7
0
b. What are the dimensions of the rectangle with the maximum area?
4x4
3.Circle the following equations if they are quadratic.
x(x-3)
p(p+12)
3x+4x
X^2+2
x(1+5)
4. The winner of the contest gets $500. Sally and her best friends are writing
a jingle for the contest. They are going to divide the money equally if they
win.
a. If n friends win, how much money will they each receive? Write an
equation.
Y=500/n
5. If your equation is x(x+3) then what does Y equal if x= 10?
100+30 =130
6. A producer sent eggs to supermarkets in 12x12x12 boxes.
a. How many eggs are in one layer of block?
12*12*12= 1728/12=144
b. What is the total number of eggs in 1 block?
12*12*12=1728
7. Write 2 equations to find the area of the rectangle.
1. x(x+2)
2. x^2 + 2x
x
x
2
8. which of these rectangles is a better deal. They cost the same and have
the same perimeter. Rectangle one is 1*9 and rectangle two is 5*5.
Rectangle two is the better deal because it has an area of 25. While
rectangle one has an area of 9. Because 5*5 equals 25 and 1*9 equals 9.