Equations:

• The quadratic parent function : y=x^2, red graph , vertex : (0,0)
• A parabola that opens up and is wider than the parent function: y=3/12(x+6)^2+2 , purple graph , vertex :(-6,2)
• A parabola that opens down and is more narrow than the parent function: y=-2x^2-2 , green graph , vertex: (0,-2)
• A parabola that has been shifted to the right of the parent function: y= 3(x-2)^+2 , blue graph, vertex:(2,2)
• A parabola that has been shifted down lower than the parent function: y= -x^2-9 , orange graph , vertex : (0,-9)

In our equations, the letters “a”, “h”, and “k” have an enormous impact on our parabolas. In our purple parabola, the letters “k” and “a” effected the shape of it as well as our direction. our purple graph is wider than our parent function, because our “a” value is 0<a<1 which caused our parabolas appear wider than our parent function and make the parabola U-shaped and has been opened upward . The “k” letter made our parabola be above our x-axis by being positive. If our “k” value was negative, our parabola would be shifted under our x-axis and our parent function. The green parabola has been opened downward and more narrow than the parent function , as well as opened above our x-axis, due to our “a” and “k” values. The “k” value is negative so our graph is under the x-axis and our parent function. Our “a” value is also negative which made our parabola open downward , and the more narrow shape than our parent function, because the value is a<-1. The blue parabola has been shifted to the right if the parent function due to the effect of the letter “h”. In the blue parabola h=+2 , so our parabola shifted two unites to the right of the parent function. The orange parabola has been shifted down lower than the parent function due to our “a” and “k” value, which are negative. “a” value made the parabola opening downward, and the “k” value shifted the parabola down, under the parent function.

1. How did you represent the same mathematical idea in multiple ways in this assignment? I used the same mathematical idea in multiple ways by understanding the definition of the vocabularies used in the chapter, as well as understanding the function and the effect of different letters( “a” , “k” , “h” ) on the parabolas and the equations.
2. State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.

The vocabulary words that I used include “y” and “x” intercepts , axis of symmetry, vertex, domain, and range

1. How did you use formatting to share your information in a clear and organized way? I used graphs, equations, and vocabulary words to write my responses for formatting my Information in a clear and organized way.