SOLUTION: 2. Write each of the following quadratic functions in the form y=ax^2 + bx + c. a) y= 2x^2 - 7 b) f(x) = 4(x-1)(x+3) =4x^2 + 2x

SOLUTION: 2. Write each of the following quadratic functions in the form y=ax^2 + bx + c. a) y= 2x^2 - 7 b) f(x) = 4(x-1)(x+3) =4x^2 + 2x - 3(Is this CORRECT???) c) 2(y-4)+7x=-3(

Question 425183: 2. Write each of the following quadratic functions in the form y=ax^2 + bx + c.
a) y= 2x^2 - 7
b) f(x) = 4(x-1)(x+3)
=4x^2 + 2x - 3(Is this CORRECT???)
c) 2(y-4)+7x=-3(x+1)^2-5
Kinda unsure of this whole question. Thanks! Help is appreciated.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
(a) is already in the correct form.
For (b), multiply the two product terms using FOIL, then multiply through by 4:
f(x) = 4(x^2 + 2x - 3) = 4x^2 + 8x - 12
[Your answer would have been correct, except you didn't multiply all the terms by '4']
For (c), carry out the multiplication and collect like terms:
2y - 8 + 7x = -3(x^2 + 2x + 1) - 5
2y - 8 + 7x = -3x^2 - 6x - 3 - 5
2y = -3x^2 - 13x - 8 + 8
So we have y = (-3/2)x^2 - (13/2)x
Let's check our answer to (c) with a simple example. Let x = 1
Original equation gives 2(y-4) + 7 = -3(2)^2 - 5 -> 2y - 8 + 7 = -12 - 5 -> y = -8
Solved equation gives y = (-3/2)(1)^2 - (13/2)(1) - > y = -16/2 = -8
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