quadratic examplesOur goal is when you are given a quadratic function you will be able to perform the necessary transformations .
Example 1 Easy
g(x)=(x-1)^2+2 First we will describe the transformations: Up 2 Right 1 Now lets begin our table This will be our parent table For our X values we will need to add 1 and for our Y values we will need to add 2.
this will make our new points: X=2 Y=3 X=1 Y=2 X=0 Y=3 Now we will graph this, the parent function is in red and the new one is in blue.
g(x)=2(x-3)^2+1
First lets list all of the transformations that will happen: Vertical stretch X 2 Right 3 Up 1 Now lets begin a table This will be our parent table Now to our X values we will add 3 to all of them because 3 is the only thing affecting our graph horizontally.
The reason we add 3 instead of subtract is because all the signs in the parenthesis are opposite. Our Y values we will multiply them by 2 then add 1. We multiply fist because we are using order of operations. Our new set of number should be: x =4 y = 3 x = 3 y = 1 x = 2 y = 3 Now we graph. Our parent graph is in red and the new one is in blue |
example 3 hard
G(x)=-1/2(-3x+2)^2-4
Do this one on your own!
Do this one on your own!
Here's what your graph should end up looking like
real life example
An object is launched at 5 meters per second from a 30 meter tall platform. The equation for the objects height s at time t seconds after launch is s(t)=-4.9t^25t+30 where s is in meters, when does the object strike the ground?