Quadratics
Important Links between Topics
In the quadratics unit, many topics link together. Here are some examples of how some topics link together:
Discriminant
The discriminant of a quadratic equation makes it easier to identify the number of zeros that a quadratic relation has. Click here to learn more about the discriminant.
Vertex Form and Graphing
Vertex form connects to graphing, since in vertex form, it is easy to find the vertex. This is because the x-value of the vertex is also the h-vlaue in the vertex form and the y-value of the vertex is the k-value in vertex form. In other words, the vertex can be represented as (h,k). Since the vertex is given in the equation, all that you need to do when graphing an equation in vertex form, is that you need to find the x-intercepts by subbing in 0 for y and then solving your equation. Once the equation is solved, the equation can easily be graphed using the vertex and the zeros. Click here to learn more about vertex form.
Factored Form, Zeros and Graphing
The equation for factored form is y = a(x+r)(x+s). In order to find the zeros using this equation, make the brackets equal to 0 and then solve for the zeros. To find zeros from factored form, no more thant 1-2 steps may be required. Also, since the zeros are already found, they could both be added and divided by two to get the axis of symmetry. Next, the axis of symmetry could be subbed into the original equation, and the vertex could be easily found. However, most of all, it is the easiest to find the zeros using factored form.
Standard Form and the y-intercept
In standard form of a quadratic equation (y = ax^2 + bx + c) the c-value is the y-intercept. Therefore, it becomes easier to find the y-intercept / the optimal value using standard form of a quadratic equation. Visit this link to see how standard form works: http://study.com/academy/lesson/parabolas-in-different-forms.html
Standard Form and Graphing
The standard form connects to grphing because when an equation is in standard form, the quadratic equation can be used to find the zeros of a parabola. With the zeros, the axis of symetry and the vertex could be found. Since at the end of finding the zeros and the vertex, you will have three coordinates of your parabola, you will be able to graph the parabola.
In general, all the forms of a quadratic relation can be used to find the vertex, axis of symmetry, optimal value and the zeros. However, some methods of getting to the same answer anre easier and faster than others. FOr example, it is easier to find the zeros in factored form than any other form.