Real world connections
At the moment many of us may assume that quadratic equations have no use outside of
school walls – our assumptions in this case, would be proven wrong. Things like
vertex form, standard form, and completing the square are used every day by
architects, businessmen, etc.
school walls – our assumptions in this case, would be proven wrong. Things like
vertex form, standard form, and completing the square are used every day by
architects, businessmen, etc.
Real Life Applications of Vertex Form
Businessmen and women who wish to maximize their revenue could use quadratics to aid their
efforts. Putting their information (such as increase in price, number of customers, etc.) into vertex
form, can help them easily identify the vertex point (p,q) , which allows
businesses to see the maximum amount of sales that will be made at the highest
price possible. Companies all around the world, such as Apple and Disney, use
this method to maximize the profit made off their products and services every year.
Businessmen and women who wish to maximize their revenue could use quadratics to aid their
efforts. Putting their information (such as increase in price, number of customers, etc.) into vertex
form, can help them easily identify the vertex point (p,q) , which allows
businesses to see the maximum amount of sales that will be made at the highest
price possible. Companies all around the world, such as Apple and Disney, use
this method to maximize the profit made off their products and services every year.
Architects can also use vertex form to their advantage, in situations like finding the
highest point on a bridge (the vertex point). They could even determine the
height above the surface of the water from a point on one of the cables on The
Lion’s Gate Bridge, a suspension bridge located in a Vancouver, seen in the
image to the left.
highest point on a bridge (the vertex point). They could even determine the
height above the surface of the water from a point on one of the cables on The
Lion’s Gate Bridge, a suspension bridge located in a Vancouver, seen in the
image to the left.
Real Life Applications of Standard Form
Standard form can also be to used determine information about revenue, but in my opinion
it’s much more useful in other real-life situations. For example when you need
to figure out the amount of time it will take for an object, like a ball or a
rocket, to touch the ground. If a rocket is shot up into the air at a certain
point you can mathematically figure out the point and time at which it will
finally touch the ground. This can be done by factoring a standard form
quadratic equation and finding your x-intercepts. The larger x-intercept, the point you didn’t start from, tells you the point at which the object will land on the ground. On the picture to the
left, the x-intercept that represents the point at which the rocket touches ground is labeled “D”.
Standard form can also be to used determine information about revenue, but in my opinion
it’s much more useful in other real-life situations. For example when you need
to figure out the amount of time it will take for an object, like a ball or a
rocket, to touch the ground. If a rocket is shot up into the air at a certain
point you can mathematically figure out the point and time at which it will
finally touch the ground. This can be done by factoring a standard form
quadratic equation and finding your x-intercepts. The larger x-intercept, the point you didn’t start from, tells you the point at which the object will land on the ground. On the picture to the
left, the x-intercept that represents the point at which the rocket touches ground is labeled “D”.
Real Life Applications of Completing the Square
Completing the square also proves to be useful in real-life situations. Say you had a
standard form equation depicting information about the amount of revenue you
want to have, but in order to know the maximum amount of sales you can make at
the highest possible price, you need to know the vertex - that’s where completing
the square comes in. “CTS” could be used to turn the standard form equation into vertex form, allowing you to see the vertex, thus providing you with the information needed to maximize profit. People like Steve Jobs, the founder of Apple, use techniques like this to set the price of their products in order ensure a maximum amount of profit.
Completing the square also proves to be useful in real-life situations. Say you had a
standard form equation depicting information about the amount of revenue you
want to have, but in order to know the maximum amount of sales you can make at
the highest possible price, you need to know the vertex - that’s where completing
the square comes in. “CTS” could be used to turn the standard form equation into vertex form, allowing you to see the vertex, thus providing you with the information needed to maximize profit. People like Steve Jobs, the founder of Apple, use techniques like this to set the price of their products in order ensure a maximum amount of profit.