Magic Math = Quadratic Functions

*Hey everyone, so today Mr. P challenged me if I can beat him at the Math Magic but as always, he won. Until now, I'm trying to figure out how he gets the right answer every time. Mr. P, I won't give up! :D*

Today we learned about Quadratic Formula. Using the quadratic formula, we can solve quadratic equations that cannot be factored.

The Quadratic Formula is

If you're asking where did the quadratic formula came from, here's how:

We can take the general form and complete the square to form the quadratic formula. Confused?

Here's the step by step derivation:

Step 1. Take the standard form or the general form and divide by a.

Step 2. Move the constant terms (the numbers that don't have 'x' variables) to the other side.
*Just move the terms that have numbers ONLY, not including numbers with 'x' beside them.

Remember! When you move the constant terms, make sure that you change their signs
(+ive/-ive)

Step 3. First, take the , divide it by 2 and square it.

since it's fraction, take the reciprocal of 2.

multiply 'b' and 2; 'a' and 2, and square it.

Step 3.1 Add to each side of the equation

Step 4. Factor the left side of the equation.

Step 5. Simplify the terms on the right side of the equation. Use the common denominator to do this. Looking at the previous one, is the common denominator.

Step 6. Take the square root of both sides of the equation.

Step 7. Subtract on both sides of the equation.

Step 8. The last step would be to simplify.

The Quadratic formula can be used to determine x-values, x-intercepts, or roots of the equation.

What you have to do to solve a quadratic equation that cannot be factored is to substitute the values of a,b and c into the quadratic formula and simplify.

For example,

The quadratic equation must be equated to zero.

Determine a,b, and c

a=3, b=7 and c=-10 *Don't forget to include the signs

Using the quadratic formula, plug in the values of a,b, and c

You have to solve both the positive and the negative of the square root. Let's do the positive first.

Solve ,, and first.

Now add 49 and 120

Take the square root of 169

Solve the numerator first and divide it by the denominator

*If there is no accurate square root of a number, write the approximate and solve as shown above.

Now the negative. *If you are comfortable solving quadratic equations using quadratic formula, you can skip steps and start from here:

Notice that the only change is the sign between -7 and 13. Instead of positive, we are going to use negative.

Now, this is not your final answer. Always remember to simplify.

And viola! You're done :)

It's really straightforward and easy. Don't hesitate to ask someone for help! :)