Red f(x)=x2 This is an example of a parent function parabola. The vertex is (0,0) because the h and k values are both 0 and together they make the vertex. The parabola opens upward because the ‘a’ value is positive 1.
Purple y=1(x-3)2 +1 This is an example of a parabola that is shifted up vertically. The vertex is (3,1) because the h value is 3 and the k value is 1. The parabola opens upward because the ‘a’ value is 1 and its opens upward when the ‘a’ value is positive. The h value is what shifted it to the right because the h value is 3. The k value is what shifted the parabola up 1 because the k value is 1.
Green y=-3(x+2)2-1 This is an example of a parabola that shifted down vertically. The vertex is (-2,-1) because the h value is -2 and the k value is -1. The parabola opens downwards because the ‘a’ value is -3 and it opens downwards when the ‘a’ value is negative. The h value is what shifted it to the left because its value is -2. The k value is -1 which shifted the parabola down 1.
Yellow y=3(x+2)2+0 This is an example of a parabola that is shifted left horizontally. The vertex is (-2,0) because the h value is -2 and the k value is 0 and together they make the vertex. The parabola opens upwards because the ‘a’ value is 3. It has shifted to the left because the h value is -2. The parabola did not move up or down because the k value is 0, therefor it cant go up.
Black y=-2(x-2)2-1 This is an example of a parabola that is shifted right horizontally. The vertex is (2,-1) because the h value is 2 and the k value is -1. The parabola opens downwards because the ‘a’ value is -2. It has shifted to the right because the h value is 2. It has also moved down 1 because the k value is -1.
Red y=-10(x+4)2-1 This is an example of a parabola that is stretched vertically. The vertex is (-4,-1) because the h value is -4 and the k value is -1 and together they make the vertex. The parabola has shifted to the left because the h value is -4. It has moved down 1 because the k value is -1. It has also been stretched vertically because the ‘a’ value is -10 and for the parabola to be narrow the a value must be greater than 1 or smaller than -1.
Blue y=1÷3(x+5)2+1 This is an example of a parabola that is compressed vertically. The vertex is (-5,1) because the h value is -5 and the k value is 1. The parabola is shifted to the left because the h value is -5. It has moved up 1 because the k value is 1. The reason its been compressed is because the a value is 1÷3 and for the parabola to be compressed the ‘a’ value must be greater than and or smaller than 1.
Communication Core Competency Reflection
I can understand and share information in a clear, organized way. I made sure my writing and graphs are are organized and neat. When creating my graph I made sure to not bunch all the parabolas together and I was also mindful to not spread them out too much. I also made sure to do a variety of different types of quadratic equations. When writing my reflection on my graph I wrote it in an organized way.
I think about what I am going to convey and to whom i will convey it to. When writing my reflection on my graphing I made sure to explain the roles of the ‘a’ ,h’ and ‘k’ values, like why the parabola was shifted left or right, why it was moved up or down, why its facing upward or downward and lastly how it is stretched or compressed.