Introduction
Quadratic equations are largely applicable to real life physics, geometry, and economics. They're essential in making graphs for analyzing economic growth or calculating the path of certain projectiles such as rockets, soccer balls, or even arrows. The objective of this project was to analyze and understand quadratic equations and how they are related to parabolas. We made connections between quadratic equations and geometry, and proved how they are related. We started with calculating the path of rockets, using geometry and algebra to find the physics displacement equation.
II: Exploring the Vertex Form of the Quadratic Equation
The vertex form for quadratic equations is useful for easily finding the x and y coordinates of the vertex of a parabola. In handouts #-# we looked at each section of the equation to find out how each value affected the resulting parabola. image For starters, the variable a defines the width and slope of the parabola. The larger the number, the steeper the incline of the parabola, and thus the smaller its width. k and h determine the vertex of the parabola.
III: Other Forms of the Quadratic Equation
There are multiple forms for quadratic equations, including vertex form, factored form, and standard form. Most of these forms can be converted into each other. You can convert vertex form into standard form, and factored into standard, and vice versa. To convert vertex form into factored form (or the the other way around), you need to first convert it into standard form. Each form is important for gleaning different information about the graph. Factored form, gives you both x-intercepts of the parabola. Vertex form
IV: Converting between Forms
I: Vertex and Standard
Vertex form can be converted into standard form by squaring (x-k): Image
You can use FOIL to achieve this; First, Outer, Inner, Last image
II: Factored and Standard
Vertex form can be converted into standard form by squaring (x-k): Image
You can use FOIL to achieve this; First, Outer, Inner, Last image
II: Factored and Standard