Math 11

Transforming Parabolas

Equations

Parent Function: y=x² My Function: y= 4(x+1)²-2

Graphing

My quadratic equation, y = 4(x + 1)² – 2, introduced multiple transformations to the parent function. It brought about both vertical and horizontal shifts, as well as alterations in the parabola’s shape. With a positive h-value of 1, the parabola shifted to the left of the x-axis, moving the vertex one unit to the left. Simultaneously, the negative k-value of -2 shifted the vertex downward by two units along the y-axis, resulting in a final vertex of (-1, -2). Moreover, the a-value exceeding 1 led to a narrower parabola.

Self Assessment

  1. In this assignment I used a verbal description and a visual graph. In a written paragraph showing my understanding of parabolas and transformations I connected it to math terms we’ve learned in class as well as the visual graph I created.
  2. In my paragraph I used the words quadratic equation, vertical/horizontal shift, vertex, to explain my understaffing of transformations.
  3. By using bolded text on each topic within the assignment I talked about, it is evident to see when a new topic starts. When creating my graph in demos I made sure there was no overlapping or messiness to it. Everything is clear and easily readable.

Facing a Challenge

The first time I tried this problem I found it challenging because I was confused as to what to do with the x squared. The first mistake I made was trying to put both sides of the equation back into the radical. There was a question just like it in group work, however it wasn’t my turn with the pen and I was just watching and observing. When I got to this workbook question I realized this was like a group work question and went back and remembered the strategy my group members came up with. I used the zero product property rule all the way back in 1.2, and factoring. I really enjoyed solving this problem because it showed how important factoring is, and how we can apply it into more complex problems. Next time I encounter a problem I will look through the notes and examples more.I try and use the examples almost as if they were a formula that I can “cut and paste” into any problem.