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:

The quadratic formula is used to solve for the x-intercept(s) or the root(s).

These roots can help you determine the position of the curve on the graph.

These roots can either be 2 different real roots, 2 of the same real roots, or 2 complex roots.

 You can determine the amount of the roots by using the discriminant.

If the discriminant is greater than zero, there will be 2 real roots.

If the discriminant is equal to zero, there will be 2 of the same roots.

If the discriminant is less than zero, there will be 2 non-real/complex roots.

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:

When an exponential equation is writen in transformational form, it is easy to find the range of that function. When finding the range of the function, first you need to find the vertical translation (VT). The vertical translation is located on the left side of the equation, (1/VS)(y-VT)=b^(1/HS)(x-HT). The Vertical Translation is also the Horizontal Asymtope (HA). The horizontal asymtope is a line that the function comes close to but never crosses. The range is either less than or greater than the horizontal asymtope. In order to figure out the range, you need to loacte the Vertical Stretch (VS). If the vertical strech is a negative number than the range will be yЄ( - ∞ ,VT). If the range is a positive number than the range will be yЄ(VT, ∞ ).

 My Exponential Graph:

My exponential equation:

Transformations:

VS= 2     HS= 1

VT= 3     HT= 1

Range (3,∞ )

Horizontal Asymtope= 3

Y-intercept= (0, 10/3)