Quadratics Essay 3
Jaquavia Jacques
Ms. Cordell
1st period
December 9, 2014
Quadratics is used to help to determine what is on a graph. There are many formulas that are used to put points on a graph to create parabolas. Parabolas are “U” shaped figures on a graph. Parabolas are examples of quadratics on a graph. Parabolas can be positioned up or down, which means if the arrows are going up it has a minimum point, and if the arrows are going down that means it has a maximum point. When graphing using the vertex formula: or the roots formula: whether the “a” is positive or negative helps identify if the graph has a maximum or minimum. Below are some examples and a visual representation of what a parabola looks like at its minimum and maximum points.
Example1:
Type Of Formula
Equation
“a” Positive or Negative
Max or Min
Vertex Formula
Negative
Minimum
Roots Formula
Positive
Maximum
There are three positions you may see a parabola when it is on a graph. Each position of the parabola determines the Nature of Roots. A parabola eithers has two real roots, one real root, or no real roots. The way you determine if a parabola has two real roots if the parabola “cuts” or cross” the x- axis in two places.
The roots formula also shows when a parabola has two real roots, which is the reason it is called the roots formula: because you can identify the two real roots by looking at the formula. To identify the roots you will set the. equal to zero, solve for x, and the results you received are your two real roots.
Determining the Roots
Example 2: State the x-intercepts Example 3: State the x-intercepts
Set equal to 0: Set equal to 0:
Solve for x: Solve for x: 3
If the parabola only touches one place on the x- axis then it only has one real root. The point you see when you determine the one real root is also known as the vertex. The vertex is the minimum of maximum point of the parabola.
Ms. Cordell
1st period
December 9, 2014
Quadratics is used to help to determine what is on a graph. There are many formulas that are used to put points on a graph to create parabolas. Parabolas are “U” shaped figures on a graph. Parabolas are examples of quadratics on a graph. Parabolas can be positioned up or down, which means if the arrows are going up it has a minimum point, and if the arrows are going down that means it has a maximum point. When graphing using the vertex formula: or the roots formula: whether the “a” is positive or negative helps identify if the graph has a maximum or minimum. Below are some examples and a visual representation of what a parabola looks like at its minimum and maximum points.
Example1:
Type Of Formula
Equation
“a” Positive or Negative
Max or Min
Vertex Formula
Negative
Minimum
Roots Formula
Positive
Maximum
There are three positions you may see a parabola when it is on a graph. Each position of the parabola determines the Nature of Roots. A parabola eithers has two real roots, one real root, or no real roots. The way you determine if a parabola has two real roots if the parabola “cuts” or cross” the x- axis in two places.
The roots formula also shows when a parabola has two real roots, which is the reason it is called the roots formula: because you can identify the two real roots by looking at the formula. To identify the roots you will set the. equal to zero, solve for x, and the results you received are your two real roots.
Determining the Roots
Example 2: State the x-intercepts Example 3: State the x-intercepts
Set equal to 0: Set equal to 0:
Solve for x: Solve for x: 3
If the parabola only touches one place on the x- axis then it only has one real root. The point you see when you determine the one real root is also known as the vertex. The vertex is the minimum of maximum point of the parabola.