testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Algebra
 Algebra 2
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

Angel1994
New Member

USA
1 Posts

Posted - 04/05/2012 :  10:25:10  Show Profile  Reply with Quote
(1-7) write each function in vertex form (8-10) write each funtion in standard form?

1) Y=x^2+3x-10
2) Y=x^2-9x
3) Y=X^2+x
4) Y=x^2+5x+4
5) Y=4x^2+8x-3
6) Y=(3/4)x^2+9x
7) Y=-2x^2+2x+1
8) Y=(x-3)^2+1
9) Y=2(x-1)^2-3
10)Y=-3(x+4)^2+1
Go to Top of Page

the_hill1962
Advanced Member

USA
1468 Posts

Posted - 04/05/2012 :  11:04:56  Show Profile  Reply with Quote
Hopefully you recognize the vertex form of an equation to a parabola as
y = a(x-h) + k
This form of the equation tells you two things:
1) If the parabola is pointing upward (when a>0) or downward (a<0)
2) The vertex point of the parabola is (h,k)

Also, hopefully you know the standard form
y = ax + bx +c
This form tells you two things:
1) If the parabola is pointing upward (when a>0) or downward (a<0)
2) The y intercept is (0,c)

The standard form also can tell you the vertex. It is a little complicated but here is a general explanation:
The quadratic equation that solves ax + bx +c = 0 is
x = ( -b +(-) (b - 4ac)) / (2a) which is saying that the solutions to the equation lie equidistant on either side of
x=-b/2a so that means the vertex lies on the line x=-b/2a
If another tutor here can draw a diagram or explain that better, please do.
That can tell you the vertex because you just plug in that value of x into the original equation and that gives the value of y and thus the vertex is (x,y).

Now, you did not show any work or state anything about how you would start doing your problems so you are either just hoping that we give you the answers or you just don't understand what is talked about above.

Here is an example of doing a problem like your (1-7):
Given y = x - 4x + 7
find the vertex form.
First, find the vertex by figuring x=-b/2a. That is x=-(-4)/2(1)=2
and then y = (2) - 4(2) + 7 = 3. The vertex is (2,3)
So the vertex form is y = (x-2) + 3

Here is an example of doing a problem like your (8-10)
Given y = (x-2) + 3
Just FOIL out (x-2) to get x - 4x + 4 and then add the 3. You get y = x - 4x + 7

The above examples were with a=1

Here is an example with a=4 (your equation 5 has a=4):
Given y = 4x + 48x +137
find the vertex form.
First, find the vertex by figuring x=-b/2a. That is x=-(48)/2(4)=-6
and then y = 4(-6) + 48(-6) + 137 = -7. The vertex is (-6,-7)
So the vertex form is y = 4(x-(-6)) + (-7)
Visa versa, if your original equation was
y = (x-(-6)) + (-7) and you need to find the standard form,
you just FOIL out (x-(-6). That is (x+6) that is x+12x+36. Multiply by 4 to get 4x+48x+144 and add the -7. That is 4x+48x+137

Edited by - the_hill1962 on 04/05/2012 13:03:57
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.06 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 14 Apr 2014