Quadratics
Quadratic Summary:
A quadratic equation represents a parabola/other shape on a graph. I will be talking only about parabolas because that is what we focused on. There are two types of equations that we learned this past week. There is the vertex equation, and the standard equation. The standard equation is basically a distributed version of the vertex. The vertex equation is in the format of y=(x+h)e2+k. If you don't know, the e2 means an exponents to the second power after the parenthesis. If you separate the equation out, y=(x+h)(x+h) +k, then you would get the x-intercepts of the parabola. You could make another equation: (x+h)=0, which would be how you get the x-intercepts. If you multiply out the vertex form, you would get y=x(e2)+hx+hx+(h*h)+k which would get you to the standard form equation, y=ax(e2)+bx+c. The (e2) again represents the exponent 2. It is really easy to go from the two forms. All you need to do is either multiply the vertex form, or you need to divide. you would do this by dividing b/2 which would get you h. Then you would take h squared and minus it from c to get k. Then you can format your equation again. I showed how bx equals hx+hx above when I multiplied out the vertex form, in case you needed proof that that would work. The xe2 equals axe2 in the other equation, the hx+hx equals bx, and he2+k equals c. The coefficients a, b, and c directly effect the parabola. If a is a positive, then the parabola has a minimum vertex, if it is negative, then the parabola has a maximum vertex. If you change b, then you change the x-intercepts of the graph, and when you change c, you change the y-intercept of the graph.
Personal Growth:
A habit of a mathematician that I applied in class with these topics would be looking for patterns. I found a lot of patterns, which was why I could make the equation of how to get x-intercepts and how to go from standard form to vertex form. I also used pattern finding to see how the parabola was effected when I changed the coefficients a, b, or c. I also stayed very organized while on these problems and proved why my work was correct. My group skills have changed with this topic because we had to work with our table groups a lot. I shared more and helped group members who were confused by what I had thought of or come up with. Also, now I am better at going up to the board and presenting my work to the class.
A quadratic equation represents a parabola/other shape on a graph. I will be talking only about parabolas because that is what we focused on. There are two types of equations that we learned this past week. There is the vertex equation, and the standard equation. The standard equation is basically a distributed version of the vertex. The vertex equation is in the format of y=(x+h)e2+k. If you don't know, the e2 means an exponents to the second power after the parenthesis. If you separate the equation out, y=(x+h)(x+h) +k, then you would get the x-intercepts of the parabola. You could make another equation: (x+h)=0, which would be how you get the x-intercepts. If you multiply out the vertex form, you would get y=x(e2)+hx+hx+(h*h)+k which would get you to the standard form equation, y=ax(e2)+bx+c. The (e2) again represents the exponent 2. It is really easy to go from the two forms. All you need to do is either multiply the vertex form, or you need to divide. you would do this by dividing b/2 which would get you h. Then you would take h squared and minus it from c to get k. Then you can format your equation again. I showed how bx equals hx+hx above when I multiplied out the vertex form, in case you needed proof that that would work. The xe2 equals axe2 in the other equation, the hx+hx equals bx, and he2+k equals c. The coefficients a, b, and c directly effect the parabola. If a is a positive, then the parabola has a minimum vertex, if it is negative, then the parabola has a maximum vertex. If you change b, then you change the x-intercepts of the graph, and when you change c, you change the y-intercept of the graph.
Personal Growth:
A habit of a mathematician that I applied in class with these topics would be looking for patterns. I found a lot of patterns, which was why I could make the equation of how to get x-intercepts and how to go from standard form to vertex form. I also used pattern finding to see how the parabola was effected when I changed the coefficients a, b, or c. I also stayed very organized while on these problems and proved why my work was correct. My group skills have changed with this topic because we had to work with our table groups a lot. I shared more and helped group members who were confused by what I had thought of or come up with. Also, now I am better at going up to the board and presenting my work to the class.