Quadratic Functions - Completing the square!

what1sth1s

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Jul 22, 2006
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Hi ok i have a big test tomorrow so here are a few questions that im stuck on. i need to do good on this test so that i can boost my failing grade to a pass! ...and could you please show me with a lot of details! big thanks!

find the vertex of the graph. in y=a(x-p)^2+q form

the fraction in there is just confusing me...
1) y=3/4x^2 + 6x + 17

Here is a word problem that your suppose to use min/max with. i am just terrible in word problems.

state the "let" and "final" statements
1) Find two numbers whose sum is 34 and whose product is a maximum.

thanks!
 
The vertex is (p, q)
Multiply by 4/3 and complete the square
I don't know calculus so I can't prove it, but it's 17*17=289

Peace and Kudos =)
 
what1sth1s said:
1) y=3/4x^2 + 6x + 17
Why is the fraction confusing? Just deal with it. We're completing the square, right?

y=(3/4)x^2 + 6x + 17

y=(3/4)(x^2 + 8x + ____) + 17 - (3/4)*_____

8/2 = 4
4^2 = 16

y=(3/4)(x^2 + 8x + 16) + 17 - (3/4)*16

y=(3/4)(x + 4)^2 + 17 - 12

y=(3/4)(x + 4)^2 + 5

Now what?

1) Find two numbers whose sum is 34 and whose product is a maximum.
This is a simple application of the previous two examples.

N = One number
Q = The other number

N + Q = 34 ==> Solve for one of them. ==> N = 34-Q
Product = N*Q

Substitute: Product = (34-Q)*Q = -Q^2 + 34*Q

There are several ways to go from here. Take your pick.
 
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