SOLUTION: Put the following quadratic function in standard form: a(x-h)^2+k. (a) f(x)=4x^2+3x+1. (b) f(x)=-2x^2-2x+3 (c) y=x^2+5x+2

Question 227665: Put the following quadratic function in standard form: a(x-h)^2+k.
(a) f(x)=4x^2+3x+1.
(b) f(x)=-2x^2-2x+3
(c) y=x^2+5x+2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started.

a)

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

So the equation is now in vertex form where , , and

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