Posted - 04/05/2012 : 11:04:56 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