Name: Josh

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:You can tell how many roots you are going to have from a quadratic equation by the descriminant in the quadratic formula. If in the descrminant there is a positive number, you will get two different real roots. If in the descriminant you have a zero, you will get two of the same roots. If in your descriminant you have a negative number than your will get two unreal roots.

How many roots you get and what they are can help you determine where your garph will fall on the plane. If your get two positive roots then your graph will either have a vertex about the x-axis and have a reflection, crossing the x-axis at two different points, or your vertex will be below the x-axis without a reflection crossing it at two different points. If you have two of the same roots this means that the vertex of your graph is located on the x-axis. If you get two unreal numbers for your roots then this means that it does not intersect the x-axuis at any point.

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: You can tell the range of the equation by looking at the tranformations on the Y in the equation. The VT will move the horizontal asymtote and the reflection will determine determine which way it moves and which side of the horizontal symptote they are one. The Y-values will always only be on one side of the horizontal asymtote and never actually touch it, just keep getting closer and closer. If the VT is positive the HA moves up and if its negative it moves down. If there is a reflection then the graph will be below the horizontal asymtote.

This is the graph of :

Transformation :

HT = 1

VT = -1

VS = 3

Reflection = yes

range: {yЄR,y<-2}

y-intercept: (0,3.5)