My Equation:
In both of these parabolas you can see the difference in the vertex and the shape of the parabola. y=x2 has a vertex of (0,0) and the axis of symmetry is x=0. The other parabola has a vertex of (-2,3) and the axis of symmetry is x=-2.
What is the significance of a, h, and, k in my equation?
In my equation the significance of a is to determine if my parabola opens upward or downward also if it is wide or narrow. If a is a negative value the parabola opens downward, if the a value is a large number it opens more narrow, and if the a value is a decimal or fraction it opens wider. In my equation since a is -4 that means it opens downward and is slightly narrow. The significance of h is to determine the x value of the vertex point. In the equation h is the opposite because of the the vertex form of the quadratic function which is f(x)=a(x-h)2+k. For example in my equation y=-4(x+2)2+3, h is 2 and in a vertex point it is (-2,3). H also represents a horizontal shift of how far left, or right, the graph has shifted. The significance of k represents a vertical shift of how far up, or down, the graph has shifted. K is also the y in the vertex point for example in my equation (-2,3) 3 is k and y.
Self Assessment
- Give an example from this assignment where you represented the same mathematical idea in three different
ways? (for example, as a graph, an equation and in words)
A mathematical idea i represented in three different ways would be my quadratic function. I showed the equation in a graph form, and equation form, and in words.
- Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
Where i used mathematical vocabulary would be horizontal shift, vertical shift, and vertex to describe h and k. I used this vocabulary to demonstrate my understanding for the significance of h and k.
- Give an example from this assignment where you used formatting to share the information in a clear and organized way.
In this assignment i used formatting to share my graph so the information would be expressed in different ways for a better understanding. I wrote out my equation to begin, showed a graph, and broke down my equation to each term for its significance.