List of Equations
- (orange) (0,0)
f(x) = x^2
- (Blue) (4,5)
f(x) = (x – 4)^2 + 5
- (Green) (-4,-6)
f(x)= (x + 4)^2 – 6
- (Purple) (-6,2)
f(x)= (x + 6)^2 + 2
- (Black) (6,-3)
f(x)= (x – 6)^2 – 3
- (Red) (-8,0)
f(x)= 2(x + 8)^2
7. (Blue) (8,0)
f(x)=1/2(x-8)^2
Transformation Explanations:
Graph 1 (orange): This is the parent function, written in vertex form as y = x^2, where a = 1, h = 0, and k = 0. The vertex is at (0, 0) and it opens upward with the standard shape.
Graph 2 (Blue): This parabola is shifted 4 units right and 5 units up, with vertex at (4, 5). The equation is y = (x – 4)^2 + 5. This is a vertical shift up and horizontal shift right. The shape remains the same because a = 1.
Graph 3 (Green): This parabola is shifted 4 units left and 6 units down, with vertex at (-4, -6). The equation is y = (x + 4)^2 – 6. It shows a vertical shift down and horizontal shift left.
Graph 4 (Purple): This parabola is shifted 6 units left and 2 units up, with vertex at (-6, 2). The equation is y = (x + 6)^2 + 2. The transformation includes a horizontal shift left and vertical shift up.
Graph 5 (Black): This parabola moves 6 units right and 3 units down, shown by the equation y = (x – 6)^2 – 3. The vertex is at (6, -3). This demonstrates a horizontal shift right and vertical shift down.
Graph 6 (Red): This graph demonstrates a vertical stretch with a factor of 2. The equation is y = 2(x + 8)^2, and its vertex is at (-8, 0). The parabola is narrower than the parent function because a = 2, and it opens upward.
Graph 7 (Blue): This graph shows a vertical compression by a factor of \frac{1}{2}. The equation is y =1/2 (x – 8)^2, with a vertex at (8, 0). The parabola is wider than the parent function due to the
Communication Core Competency Reflection
During this task, I displayed communication by keeping my equations neat and using Desmos to graphically illustrate how each transformation changes a parabola. I used color coding, spacing, and labeled points to make my graph understandable. I took the time to think about how to explain the transformations using proper math and sentence. I also considered my teacher and peers by maintaining a clean layout and professional writing. This allowed me to clearly and briefly present my thoughts.