PART 1: QUADRATIC EXPLANATION
STANDARD FORM OF A QUADRATIC
The Quadratic form is something we have been heavily studying on for sometime now. The basic form is written y=ax^2+bx+c. Through our studies in this field we have learned many tips and tricks that can help us solve any equation we are faced with as well as critical pieces of information to plot our own graph. Some of the Tips/ tricks we learned to solving these equations where that “c” always equaled the y intercept or (0,C). And example of this would be [5x^2+7x+4]. If we were to put this equation into a graphing program we would see that the y intercept is infact 4.
A, B, and C on the graph
y=2x^2+4x+12
y=-2x^2+4x+12
y=2x^2+4x-12
y=-2x^+4x-12
y=-2x^2+4x+12
y=2x^2+4x-12
y=-2x^+4x-12
From looking at this graph we can identify a few select rules or tricks on how to solve it. For example as you can see for the first equation up there the vertex is (-1, 10). This probala is facing down. The reason for this is the positive exponent in front of the x^2 [a]. The same can be said for the third equation. But for the second and third equation you can see the the probala is facing down. The reason is similar to the first explanation above. The exponent is a negative they're for it faces down.
the vertex
An equation we have used in finding the vertex is y=a(x-N)^2+M. If you plug in your variables to this equation you will find that N,M is your vertex. This Vertex form is in exact correlation with
y=ax^2+bx+c.
y=ax^2+bx+c.
The "x" intercept
The x intercept is the crossing point of the probala and the x axis. It is also called the root, or zero. In many quadratic equations the probala crosses the x axis twice. But it can also cross the y axis just as many times.
There and back again (a vertex to standard journey)
To go to vertex
x^2+40+0
(x+20)(x+20)
(x+20)^2+400
To go to standard
(x+20)^2+400
(x+20)(x+20)+400
x^2+20x+20x+400-400
x^2+40x+0
x^2+40+0
(x+20)(x+20)
(x+20)^2+400
To go to standard
(x+20)^2+400
(x+20)(x+20)+400
x^2+20x+20x+400-400
x^2+40x+0
conclusion
During this 10th grade unit I have grown in a lot of ways. At my middle school, elementary school, and even in my life I have never had to think the way I do here. At High tech high NC you are encouraged to to think differently about questions, projects, and even test (though they are not encouraged). In math we do things called open ended problems. They require you to do lots of other thinking about this problem because there is an infinite number of answers. In this way I have grown. I have learned to take a few steps back and looks at things in a different way.