Name: Hilary

Task #1

Question: What can you tell about the graph of a quadratic function based on the roots you get from solving the quadratic formula for that equation?

Answer: When using the quadratic formula, you are able to solve for the x-intercept(s) or the root(s). Before using the quadratic formula you are able to use the discriminant, which is

. This equation comes from the quadratic formula, it is the information below the square root sign. This equation can help you to know the following: if the       discriminant is greater than 0; their will be 2 real roots, if the discriminant is equal to 0; their will be 2 of the same roots, and if the discriminant is less than 0; their will be 2 non-real roots. Finally to find the exact numbers for the x-intercepts you will use the quadratic formula, which will give you two values.

Equation: 

Task #2

Question: How can you tell, by looking at an exponential equation in transformational form, what the range of the function is?

Answer: The range of a function can be found easily when the exponential equation is writen in transformational form. The first step when finding the range is to find the vertical translation (VT) in the equation (1/VS)(y-VT)=b^(1/HS)(x-HT).  The vertical translation is equal to the horizontal asymtote, which is the line that the function approachs but never touchs, leaving the range to be less than or greater than the horizontal asymtote. In order to find out if the equation is less than or greater than the horizontal asymtote, you must locate the vertical stretch. If the vertical stretch is a positive number than the range will be yЄ(VT, ∞ ) and if the vertical stretch is a negative number than the range will be yЄ( - ∞ ,VT).

Graph:

Exponential function is transformational form: 

VT =  -5                    HT = 4

VS =  40                   HS = 1

y-intercept: 2

horizontal asymtote: 1

range: yЄ(1, ∞ )