The Introduction:
In math class we were launched a new project called " The Quintessences Of Quadratics" . This projected is based on the worksheets we been working on during class. We had many options on what worksheets we wanted to focus on like, Kinematics-projectile motion, Geometry-triangle problems and rectangle problems, Economics-Maximizing revenue/profit or minimizing expenses/losses. I found most of them pretty challenging so I wasn't which one was the best for me to focus on.
Exploring The Vertex Form Of The Quadratic Equation:
I decided to go for "Finding the vertices and intercepts" on the quintessence of quadratics packet . I found this math topic pretty challenging because I wasn't sure where to start. It was asking to write:
* The function In vertex form
* Find the Vertex Of The graph of the function
* Write an equation and solve it to find the x-intercepts
I started off writing down the equations and added the parenthesis to the equations which were:
1. y= x^2 +4 x+3
2. y= x^2-6 x+12
3. y=-x^2 + 8 x + 9
4. y=-x^2 -2 x + 4
Handouts and Desmos " a,h and K"
The way a,h & k parameters affect the location and shape of a parabola is when "h and K" is the vertex which would be y=a(x-h)2 +K. And " A is in the vertex form as in y=ax2 + bx +c. The relationship between quadratic equation and a parabola is when they both plot the graph of a quadratic relation that shows the significant points on the graph.
There was about 3 different ways to change the graph lines. For example this image shows how wide and thin the line could get, y=x2 makes the line wider, y=2x2 makes the line thin and then y=3x2 would make the liner thinner, it all depends on how big or small the number is and format.
Other Forms Of the Quadratic Equation
the other forms of the quadratic equation are Standard form: y=ax^2 + bx + c
form and Factored form: y=a(x-h)^2.
Other Forms Of the Quadratic Equation
the other forms of the quadratic equation are Standard form: y=ax^2 + bx + c
form and Factored form: y=a(x-h)^2.
Converting between forms
-Convert from vertex form to Standard form
-Convert from standard to Vertex form
The graph is showing 2 lines that connect with each other. The two different equations have been converted to give the same line graph.
-Convert from vertex form to Standard form
-Convert from standard to Vertex form
The graph is showing 2 lines that connect with each other. The two different equations have been converted to give the same line graph.
The standard form is solved differenty than the vertex form. I was familiar with this type of equations because I used to work on problems like these during class and we also had worksheets that involved these type of math problems. The equation was y=2x^2 +-4 and I ended up with y=2(x^2 -1/2x)-4.
This is a vertex form equation and it's solved way different than the standard form equations. You could see that I didn't isolate x. Instead I factor the equation which came out to y=2(x+ 0.4) (x. +0.4) -4 and ended with y=2x^2 + 1.6x-3.68.
Reflection:
When I was first introcuded to this project, I wasn't sure how to start it off. I struggled with it because i wasn't sure what we had to do until I asked my teacher about it. I started off picking a problem off my quintessences Of quadratics math packet and I ended up picking number 21 " Finding the vertices and intercepts" I picked this worksheet because I understood it better than the other problems on the worksheets. It took me about 3 days to figure out how to start it because I was stuck and aslo had to worry about other things. I beileve this is going to help me in the future and on my SAT.
When I was first introcuded to this project, I wasn't sure how to start it off. I struggled with it because i wasn't sure what we had to do until I asked my teacher about it. I started off picking a problem off my quintessences Of quadratics math packet and I ended up picking number 21 " Finding the vertices and intercepts" I picked this worksheet because I understood it better than the other problems on the worksheets. It took me about 3 days to figure out how to start it because I was stuck and aslo had to worry about other things. I beileve this is going to help me in the future and on my SAT.