How Do You Convert a Quadratic to Standard Form?

[willywonka12345]

Quadratic in standard form help...please

Homework Statement

Write the quadratic function f(x) = x^2 + 3x + 2 in standard form.

Homework Equations

Standard form equation : f(x) = a(x-h)^2 + k

The Attempt at a Solution

Ok, I think I got this one but am wanting to be sure.

I set it up : (x^2 + 3x + 2.25) + 2

then get : (x + 1.5)^2 + 2 - 2.25

then get as answer : f(x) = (x + 1.5)^2 - .25

Is this what you all get ?

I really appreciate any help.

 

[neutrino]

Where did the 2.25 come from?

 

[cristo]

Homework Statement

Write the quadratic function f(x) = x^2 + 3x + 2 in standard form.

Homework Equations

Standard form equation : f(x) = a(x-h)^2 + k

The Attempt at a Solution

Ok, I think I got this one but am wanting to be sure.

I set it up : (x^2 + 3x + 2.25) + 2

then get : (x + 1.5)^2 + 2 - 2.25

then get as answer : f(x) = (x + 1.5)^2 - .25

Is this what you all get ?

I really appreciate any help.

That looks fine to me. If you want to check in future, expand out the bracket, and simplify. What you get should be equal to the original expression.

Edit: I didn't read any lines other than the last one! The final answer is correct, however the method doesn't make much sense (I'm glad someone's on the ball, neutrino! )

 

[willywonka12345]

Where did the 2.25 come from?

Take half of three and multiply it by itself.

 

[willywonka12345]

Thanks cristo ! I am checking it now. It works out :) Thanks for the tip.

 

[neutrino]

Take half of three and multiply it by itself.

Okay, but it can't magically appear from nowhere, can it? You add and subtract that amount, so that the expression x^2+3x+2 +2.25 -2.25 is equivalent to x^2+3x+2.