Graph A: Quadratic parent function π(π₯)=X^2
Graph B: Shifted up π(π₯)= (x-6)^2+2
Graph C: Opens up and is wider π(π₯)= 1/3 (x+7)^2 -5
Graph D: Opens down and is more narrow π(π₯)=-10(x-5)^2
Graph E: Shifted down π(π₯)=-(x+1)^2-1
A, H, and K all play significant rolls in where the parabola is and the shape that it has. The A coefficient determines the direction and width of the parabola. If A is positive the parabola opens upwards; if A is negative it opens downwards. A affects the width of the parabola; the larger the value the narrower the parabolas is. Graph C has a width larger than the parent function which means the coefficient of A is between 0-1. The value of H moves the parabolas left or right on the graph. It represents the x-coordinate of the vertex. Thus, meaning if H is positive the parabola is shifted to the right, and if it is negative it is shifted to the left. Graph D represents a positive value of H, because it has shifted to the right of the parent function. The value of K shifts the parabola up or down. It corresponds with the y-coordinate of the vertex. A positive K moves the parabola upward and a negative K moves it downward.
Self Assessment
- In this assignment I was able to approach the concept from different angles to deepen my understanding. I used algebraic explanations, in the paragraph explain the significance of A, H, and K. Furthermore, I created multiple parabolas to showcase the geometric transformations of the parabolas. Taking the information that was given in text I created functions that better showcase the purpose of A, H, and K.
2. Throughout this assignment I used mathematical vocabulary such as, vertex, coefficient, shift, function, positive, negative, and coordinate. Using the mathematical vocabulary I was able to create a clear and understandable paragraph that explains the importance of A, H, and K.
3. I was able to format this assignment in an organized way to make it clear and easy to read. Furthermore, I clearly labeled and coloured coded my graphs to make it easier to follow. Also, I used headers and bolding writing to separate unlike text.