Task One

Name: Gina

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:  The quadratic formula will tell you how many roots or x intercepts you can have. If you use the discriminant you will be able to find the different types of roots you will get. If the discriminant is >0 you will have 2 real roots, if the discriminant is <0 you will get 2 non-real roots because the square root of a negative number is non-real or imaginary. If the discriminant is = to 0 then you will have 2 roots that are equal to each other because if you add or subtract zero it gives you the same value.

Task Two

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

Answer: The only things that affect the range of an exponential equation is the vertical translation and the vertical stretch. The value of y (the VT) is the horizontal asymptote. The horizontal asymptote is the line that the function approachs but never touchs. If the vertical stretch is a positive number, then the range will be from the horizontal asymptote to positive infinity. If the vertical stretch is negative, then the range will go from negative infinity to the horizontal asymptote.

Equation:

VT= 1     HT= 1/2

VS= 3     HS= 1

y-intercept: 2.06

horzontal asymptote: y=1

range: (1, ∞)

Graph: