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How do you draw a quadratic function without plugging in numbers and plotting points?

 May 1, 2014

Best Answer 

 #2
avatar+118723 
+5

CPhill gave you lots of great ideas.

If you want to plot   $$y=x^2+5x+4$$   without plotting a whole lot of points this is the best way.

First the y intercept is where x=0 so substitute in x=0 and you will get y=4 (the number tacked on the end- this is called the constant) 

This in not an overly important point to find but it is very easy to find (0,4)

Now lets look for some important points.  If they exist we want to find the x intercepts these can also be called the roots or less often the zeros of the equation.  You can factorise and find them that way or you can find them using the quadratic equation.

I'm going to factorise.  I need 2 numbers that multiply to 4 and add to 5. That is easy, 4 and 1

$$y=(x+4)(x+1)$$    I want the answers when y=0  (That is the equation of the x axis)

$$0=(x+4)(x+1)$$     If 2 things multiply to give zero then one of them must be zero.

x+4=0   or   x+1=0

x=-4 or x=-1

Thes are the roots so plot them.

 now parabolas are symetrical so the axis of symmetry must be

 $$x=\frac{-4+-1}{2}\\

x=\:-2.5$$

Find the vertex by sub'ing in x=-2.5 to find the y value

Then you have the vertex and 2 roots and that is enough to fully define your parabola.

 May 1, 2014
 #1
avatar+130511 
+5

Re: How do you draw a quadratic function without plugging in numbers and plotting points?

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If you're taking Algebra, you will probably learn how to do some of this. If you take Pre-Calculus or Calculus, you will learn many other techniques that will enable you to "see" what a particular quadratic might look like. Barring that, unless it's a "basic" graph, you might have to be stuck with plotting (some) points. This could become tedious.

Here's a site where you can look at the graph of any quadratic (or any other polynomial in one variable) you specify:

 

http://www.wolframalpha.com/examples/PlottingAndGraphics.html

Just click into the first "box" - "plot a function of one variable" - and it will take you to a page where you can key in your function and see a graph of it !!!

P.S. .......there's a lot of other interesting "stuff" on this page, too!! Explore some of it !!

 May 1, 2014
 #2
avatar+118723 
+5
Best Answer

CPhill gave you lots of great ideas.

If you want to plot   $$y=x^2+5x+4$$   without plotting a whole lot of points this is the best way.

First the y intercept is where x=0 so substitute in x=0 and you will get y=4 (the number tacked on the end- this is called the constant) 

This in not an overly important point to find but it is very easy to find (0,4)

Now lets look for some important points.  If they exist we want to find the x intercepts these can also be called the roots or less often the zeros of the equation.  You can factorise and find them that way or you can find them using the quadratic equation.

I'm going to factorise.  I need 2 numbers that multiply to 4 and add to 5. That is easy, 4 and 1

$$y=(x+4)(x+1)$$    I want the answers when y=0  (That is the equation of the x axis)

$$0=(x+4)(x+1)$$     If 2 things multiply to give zero then one of them must be zero.

x+4=0   or   x+1=0

x=-4 or x=-1

Thes are the roots so plot them.

 now parabolas are symetrical so the axis of symmetry must be

 $$x=\frac{-4+-1}{2}\\

x=\:-2.5$$

Find the vertex by sub'ing in x=-2.5 to find the y value

Then you have the vertex and 2 roots and that is enough to fully define your parabola.

Melody May 1, 2014

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