Explanation

In the formula y= a(x-h)^2 +k , ‘a’ determines the width and direction of a parabola‘s opening. The parabola becomes more compressed than the parent function if a>1. The parabola becomes more stretched than the parent function if a<1. In my given equation, a= -2. The ‘a’ is a negative therefore it flips and opens downwards. If the ‘a’ in my equation was a positive, the parabola would open upwards. ‘h’ tells us the shift of the parabola horizontally. If ‘h’ is negative (-) it shifts to the left. Likewise, if ‘h’ is positive (+) it shifts to the right. My h= -7 therefore it shifts to the left. The vertical shift of the parabola is determined by the value of ‘k’. If ‘k’ is a negative (-) it shifts down, if ‘k’ is a positive (+) it shifts up. k= -2 in my equation therefore it shifts down. In addition, both ‘h’ and ‘k’ also tells us the vertex of a parabola. ‘h’ gives us the x value of the vertex while ‘k’ gives us the y value of the vertex.

Self- Assessment

I was able to represent the mathematical idea in words and in a graph. For this assignment, I made sure to be able to explain the significance of a, h and k using mathematical vocabulary. I made sure to incorporate words such as compressed and stretched to describe parabolas. I was able to accomplish this by referring to the notes. I remembered to show both parent function and my equation graphed to show a visual representation of both equations to give proper understanding. I properly showcased my graphs and ensured that they were the appropriately cropped and sized.