Through out this project we learned so many different things starting with Pythagorean thorium, projectile motion, and areas and volume. All of that was to help us better understand how to do quadratic functions. In the process of doing this project we also learned how to use algebraic symbols. We learned that when you write out a quadratic equation in different ways like vertex form or factored form it shows the graph of the function better.
Exploring vertex form. In the beginning of this project we used a website called Desmos and that was so we could better understand parabolas. we were also handed work sheets to help us under stand better. All of this was so we could see how they affect the location and shape of a parabolas. We used a formula that was y=a(x-h)^2+k and we put it into Desmos, This formula would move different ways, if we made it have a number higher than one it would be skinnier but if it was a negative number it would be opposite and it would flip upside down. if i change H to a Positive or Negative number it would move left or right on the graph and if i change K to a positive or negative number it would move up and down the graph.
Other forms of quadratic equations
The standard form of the quadratic equation 2x^2 = x+4 is 2x^2 -x-4=0
Converting between forms
the pictures below are factored form to standard form, standard form to vertex form and vertex form to standard form
Solving problems with quadratic equations
There are a few real world things i could solve with quadratics
The first being Throwing a ball or rock, You throw it up in the air and it slows down as it goes up, then when it comes down it goes faster and faster. if you throw a fall 3 meters above the ground with 20 m/s, when will it hit the ground?
the second being Is a satellite dish, or reflecting telescope, the shape of it is defined by a quadratic equation
the third being economics
Reflection
over all this quadratics unit was very challenging at first, but I have learned a lot from it and I had some fun with it too. The main reason i like this so much is because i have never seen this type of math before so it was completely new to me and it I also felt like it was the most relate able to the real world because a lot of math that we do in school seems like we never use it in real life but quadratics you do, and you do it a lot even if you don't realize it.