My Equation, and the Parent Function

h, k, a? What Are They?

What do the values of “h”, “k” and “a” in the equation y=a(x+h)^2+k mean? And how do they change and transform the parabola from the parent function?

To begin, the value of “h” is the horizontal shift, (easy to remember! “h for horizontal”). Remember that if the parabola is shifted to the left (or negative side of the graph) “h” will be positive. If the parabola is to the right (positive side of the graph), “h” will be negative. The value of “h” also gives is the “x” point of the vertex.

The value of “a” is a coefficient that controls all of the stretching and compressing. If a>1 the parabola will be more compressed (narrower) than the parent function. If a<1 the parabola will be more stretched (wider) than the parent function. If a is negative, the parabola will reflect down, if a is positive, the parabola will open upwards.

Lastly, the value of “k” is the vertical shift. If “k” is positive, the parabola will be shifted up. If “k” is negative, the parabola will be shifted down. The value of “k” also gives us the “y” point of the vertex. “h” and “k” together give us the entire vertex.

Specifically in my equation:
In my equation (y=-1/4(x-5)^2 -5) the “a” value is negative, and less than 1. This means, my parabola will reflect down, and be wider than the parent function (as shown in the Desmos graph below). In my equation the “h” value is negative 5 meaning, the parabola is shifted 5 spaces to the right from the parent parabola (as shown in graph below). The “k” value is also -5 meaning the parabola will be shifted 5 spaces down from the parent function, (as shown below).

Self Reflection

1. Give an example from this assignment where you represented the same mathematical idea in multiple ways? I represented the values of h, k, and a in 3 ways. In words and explanation, in graph form, and in numerical, mathematical form.

2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding. In all of my explanations I used mathematical vocabulary like, stretched, compressed, parent function, transformed, shifted, reflected, less than, and a few more.

3. Give an example from this assignment where you used formatting to share the information in a clear and organized way. I formatted my Desmos graph to show both my equation and the parent function so while I was explaining, the reader had a chance to visualize this. For this reason (another formatting situation) I posted my graph twice.