SOLUTION: Hi, could i please have some help with this question, thank you in advance. Write a paragraph explaining how a quadratic function can be graphed by applying transformations to {

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, could i please have some help with this question, thank you in advance. Write a paragraph explaining how a quadratic function can be graphed by applying transformations to {      Log On


   

Question 856847: Hi, could i please have some help with this question, thank you in advance.
Write a paragraph explaining how a quadratic function can be graphed by applying transformations to f%28x%29=x%5E2. Fill in the blanks below.
The graph of a quadratic function g%28x%29=a%28x-h%29%5E2%2Bkcan be plotted from the function f%28x%29=x%5E2by applying transformation properties.
- The parameter a _____________________________________________.
- The parameter h affects the ______________________________ translation and moves the graph to the right if __________ and to the left if __________.
- The parameter k affects the ______________________________ translation and moves the graph up if _________________ and down if ______________.
- The vertex is located at ________________________________________.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The trickiest part to learn at first is what happens when you add or subtract a value to x. You already know that the vertex of f%28x%29=x%5E2 is at (0,0). If you change to f%28x%29=%28x-3%29%5E2, then you want to know where does the vertex and the rest of the graph go? Consider x=3. This makes f%28x%29=%283-3%29%5E2=0%5E2=0. No change has been done to y, only changed was in x. We moved x three units rightward when we SUBTRACTED 3 from independent variable x.


(Here, h is assumed a positive number): That is a representative example to show that f%28x%29=%28x-h%29%5E2 is the same shape as f%28x%29=x%5E2 but moved h units to the right. Pay attention to the operation symbol used. %28x%2Bh%29%5E2 is the same as %28x-%28-h%29%29%5E2 and this would represent, if h itself were a positive number, h units movement to the LEFT.

The factor, a, shrinks the graph vertically if abs%28a%29%3C1, but stretches the graph vertically if abs%28a%29%3E1.