1. y= x^2 Vertex is (0,0)

2. y= 3(x+5)^2 – 1 Vertex is (-5,-1)

3. y= – 6/7 (x-5)^2 + 2 Vertex is (5,2)

4. y= (x+5)^2 Vertex is (-5,0)

5. y= x^2 – 4 Vertex is (0,-4)

My red parabola is a parent function that has no k-value, making it the simplest form of a family function. This makes all of the parabolas properties equal to all real numbers and that they will all be positive. My black parabola is going downwards because the value of a is less than zero. The black parabola is also narrower and vertically stretched because |a|>1. My blue parabola is opening wider because the -6/7 is 0<|a|<1, making it shorter and wider (vertically compressed) than the parent function. My green parabola has no k, making it have no y-interception. The h is -5, making the parabola sit in the negatives on the x-axis. My purple value has the vertex of (0,-4) which makes my point of symmetry at -4 on the y-axis, Which makes the given minimum value to be y≥-4.

Self-Assessment

I represented the same mathematical idea of parabolas in multiple ways in this assignment by creating multiple equations that are significant to parabolas. Using DESMOS, I was able to graph such parabolas, this helped my formatting to be clear and meaningful. Some relevant mathematical vocabulary I used was vertically compressed which means the parabola will be shorter and wider than usual. The y-axis is the vertical coordinates on a graph, and the x-axis is the horizontal coordinate on a graph. My blue sentence demonstrates a full sentence using mathematical vocabulary. I found these definitions in my notes that I had taken and I remembered some of the definitions from prior lessons.