Solving Quadratic Functions

DEF: A quadratic function is a function in the form of Ax^2+Bx+C=y where A, B and C are and real number (with A not equal to zero) and x and y are variables.

What a quadratic function looks like when graphed
SOLVING

STEP 1: Standard Form

In order to solve a quadratic equation the first thing you must do is to get the equation in to standard form.

Step 2: Taking Care of Y

As you may have noticed in the video above there was no y variable in the equation. That's because when we begin solving a quadratic equation after we get the equation in standard form we replace y with 0. We do this because when we say "solving a quadratic equation" what we really mean is that we are finding values of x that make y equal 0.

Step 3: Factoring

This is where things can get a little tricky. Today we're going to focus on the situations where A is 1.

1st, get the equation in standard form

2nd, take care of y

3rd, we know that quadratic equations result from the multiplication of two terms of the form (x+J) or (x+K) where J and K are any real number.

4th, we need to find J and K. These numbers are special because they multiply to be C (in this case -18) and add to B (in this case 3). So we must first write out the factors of -18.

The next step (unnumbered, my bad), is to find the factor pair of -18 that add to be 3.

The 5th and final step in factoring a quadratic equation (where A is 1) is to write the equation in the (x+J)(x+K)=0 form.

Step 4: Zero Divisor Property

According to the Zero Divisor Property if A*B=0 then either A=0 or B=0. This concept applied to quadratic equations looks like:

Zero Divisor Property applied

That is to say that if (x+J)(x+K)=0 then it is fair to say x+J=0 and x+K=0. If we independently solve these equations for x we get two possible values for x.

Step 5: Checking Our Work

Substituting our answers back in

Checking you pr work is very important. This ensures your answer is correct. As shown above both our answers are correct. That's right quadratic equations can have two correct answers! This makes sense when you think about their graph: there are two x intercepts.

Note the location of the x intercepts

Here is a video summing up this presentation and giving a sneak peek of our next lesson, which will be over when A is not 1.

Credits:

Created with images by Unsplash - "concert performance audience" • WFWmKent - "wfw_quadratic" • Wokandapix - "calculator math mathematics"

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