y = a(x – h)² + k

y = x²
(0, 0)

y = x² + 5
(0, 5)
y = x² – 5
(0, -5)


y = (x – 6)² + 2
(6, 2)
y = (x + 6)² + 2
(-6, 2)


y = ⅓(x – 12)² + 5
(12, 5)
y = 4(x + 12)² + 5
(-12, 5)


y = -(x – 6)² – 2
(6, -2)
y = -(x + 6)² – 2
(-6, -2)

The black parabola is the parent function and is displayed on the graph unaltered. The values of a, h, and k are all 0.

The green parabolas are elevated and sunken along the y-axis by 5. This is because the k value was changed to +/- 5. By changing the value of k, the vertex of the parabola travels up or down, changing it’s height.

The orange parabolas are moved left and right by changing the h value. By changing the value of h to 6, which appears like -6 in the formula y = a(x-h)² + k, the parabola moves 6 to the right. The inverse happens with -6, appears like +6, as the parabola will shift 6 to the left.

The purple parabolas are wider and skinnier based on the change in the a value. If |a| ≥ 1, then the parabola becomes skinnier based on value of a. For example, a = 4 will be narrower than a = 2.
If 0 ≤ |a| ≤ 1, then the parabola will open wider. The width of the parabola is based on the value of a. A parabola with a = 1/9 will be much wider than a parabola with a = 9/10.

The red parabolas have been flipped upside down by changing a to a negative value. If a is a positive value, the parabola will open up and if a is a negative value, the parabola opens down. The other rule of a still applies.

Communication Core Competency Reflection

In this assingment, I demonstrated how I can understand and share information in a clear and organized way by presenting my ideas in a logical way. I made sure to use clear and proper mathematical language to help the reader understand the different alterations that a parabola can undergo. I thought about what I was going to convey before I started. This helped me set my tone and choose my example parabolas to make my work more understandable.