Quadratic in standard form help please

This is so that the bracket is a perfect square. The classic example is completing the square for x^2+3x. You take 3/2 and add it and subtract it, so you get x^2+3x+9/4-9/4 = (x+3/2)^2-9/4.\nIn summary, the conversation was about completing the square to write a quadratic function in standard form. The final answer given was f(x) = (x + 1.5)^2 - .25, which was obtained by adding and subtracting 2.25 to make the bracket a perfect square.
  • #1
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 ? :smile:

I really appreciate any help.
 
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  • #2
Where did the 2.25 come from?
 
  • #3
willywonka12345 said:

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 ? :smile:

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! :smile: )
 
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  • #4
neutrino said:
Where did the 2.25 come from?

Take half of three and multiply it by itself.
 
  • #5
Thanks cristo ! I am checking it now. It works out :) Thanks for the tip.
 
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  • #6
willywonka12345 said:
Take half of three and multiply it by itself.
Okay, but it can't magically appear from nowhere, can it? :wink: 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.
 

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

How do you convert a quadratic equation to standard form?

To convert a quadratic equation to standard form, you need to rearrange the terms so that the equation follows the format of ax^2 + bx + c = 0. This may involve combining like terms and moving all terms to one side of the equation.

What are the steps for solving a quadratic equation in standard form?

The steps for solving a quadratic equation in standard form are as follows:
1. Rewrite the equation in standard form if necessary.
2. Factor the equation or use the quadratic formula to find the solutions.
3. Check your solutions by substituting them back into the original equation.
4. Write the solutions as ordered pairs if necessary.

Can the leading coefficient of a quadratic equation in standard form be negative?

Yes, the leading coefficient of a quadratic equation in standard form can be negative. This will not change the shape or position of the parabola, but it will affect the direction in which the parabola opens.

What is the significance of the discriminant in a quadratic equation in standard form?

The discriminant in a quadratic equation is the part of the equation under the square root sign, b^2 - 4ac. It is used to determine the nature of the solutions of the equation. If the discriminant is positive, there are two distinct real solutions. If the discriminant is zero, there is one real solution. If the discriminant is negative, there are no real solutions.

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