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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.