Week 6: Solving using the Quadratic Formula

This week in Pre Calculus 11 I learned a few things that really helped me. I learned how to recognize perfect square trinomials, how to use the box method to factor, and how to use the quadratic formula when solving.

I will quickly go over each of these things.

Perfect Square Trinomials 

ex. x^2 + 10x + 25

Always notice the first and third terms

  • 1st term: x^2
  • 2nd term: 10x
  • 3rd term: 25

Notice that x^2 and 25 are perfect squares

\sqrt{x^2} = x     and    \sqrt{25} = 5

The 2nd term will always be 2\sqrt{1st}\cdot\sqrt{3rd}

ex. 10x:

  • 2\sqrt{x^2}\cdot\sqrt{25}
  • 2\cdot5\cdot{x}
  • 10x

This is how you recognize perfect square trinomials

Box Method (Factoring)

This box method is typically used with ugly polynomials but can be used with any expression. You want to be careful about using this method because the numbers could get big.

ex. 5x^2 + 9x + 4

Step 1: Insert the 1st and 3rd term into the box,

Top left box: This is where you would put the first part of the expression. ex/ 5x^2

The bottom right box: This is where the last part of your expression would go. ex/+ 4

Step 2: Multiply the 1st and 3rd term and find the products

Step 3: Chose the pair that would +. – to the 2nd term

Step 4: Insert them into the box.

* Doesn’t matter which one empty box they’re put in

*take out what is common horizontally and vertically

Step 5: Insert into the brackets and expand to check

This is how you use the box method

Quadratic Formula 

The quadratic formula can be used to solve any quadratic equation. This can be a really useful and quick way to solve an equation. 

ex/ $latex 3x^2 – 4x -1 = 0 %

Step 1: Determine a, b, and c and substitute into the equation.

  • a = 3x^2
  • b = -4x
  • c = -1

substitute into the quadratic formula.

Step 2: Simplify the radicand

Step 3: Simplify the radicand further

Step 4: Divide by the common denominator to get it into simplest form

This is how you use the quadratic formula

Today we learned how to recognize perfect squares trinomials, how to use the box method, and how to use the quadratic formula.

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