My Equation: 𝑦=4(𝑥+1) ²−2
Modifying “a” made the parabola appear wider or thinner. In other words, when a > 1, the graph compresses. When 0 < a < 1, the graph stretches. You can even determine whether the graph opens upwards or downwards based on this number.
“h” represents a horizontal shift of how much the graph moves left or right from x = 0. While “k” represents a vertical shift of how much the graph moves up or down from y = 0.
A as 4 on my parabola made my parabola thinner, k changed the vertex of my parabola by 1 to the left and h altered the parabola by moving the vertex 2 down.
Self Reflection
I represented the same mathematical idea in 3 different formats. The way in which I presented this idea in 3 different ways was through an equation which is y= 4(x+1)2 -2, then in words explaining how the graph can get wider and narrower based on the value of “a” in the model equation represented by y=a(h-x)2+k, or how the graph can be moved right or left based on the value of “h” in the model equation or how the parabola vertex is changed by the value of “k”; and the third way is by the graph as above with the basic one in blue, and a second one based on my equation has changed to the one in red.
When explaining my parabola in words I used mathematical terms like vertex shift on the y-axis, vertical and horizontal shifts on the x-axis to represent my understanding of a, h and k in an equation.
I used formatting to help get my point across. I did this by making my parabola red vs the standard which is blue.