Transforming Parabola

The orange graph in the image above show’s the parent function y=x^2, this is the base equation for graphing a parabola. The light blue parabola uses the equation y=-7x^2. The new coefficient is a, the base equation would be y=ax^2. The a represents the change in width and which direction the parabola opens. If a equaled a positive number the parabola would open the opposite way like in the first image. Another change is if the number was a fraction which would make it wider. The next equation is y=3(x-4)^2 which is the green parabola. This adds the variable h to the equation which shifts the parabola horizontally on the x axis. The base equation would be y=a(x-h)^2. If the number is a negative in the equation the parabola will shift right and opposite if its a positive in the equation, this is because the base equation has h as a negative meaning that when h equals a positive it would still be (x-h)^2. h also is the x value in the vertex. The last parabola is the purple one and has the equation y=5(x+7)^2+3. The last variable is k, the base equation would be y=a(x-h)^2+k. The variable k shifts the parabola vertically on the y axis. if the number is positive it will move up and if negative it will move down. k also equals the y value in the vertex.

Self Assessment

How did you represent the same mathematical idea in multiple ways in this assignment?

Even though the equations were different they all used the parent function and every time i added something new it stayed into the next equation as well.

State some of the relevant mathematical vocabulary words you used to demonstrate your understanding and their definitions. State where you found the definitions (your own memory, class notes, online?)

I used words like horizontal, vertical, shifts, y/x axis to make sure people know how the parabola is moving on the graph.

How did you use formatting to share your information in a clear and organized way?

I added the variables one at a time so the explanation were less chunky and had different pictures for each parabola so you can really focus on the specifics for the parabola.

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