Week 7 – Pre Calc 11 – Solving Quadratic euqtions with quadratic formula

This week in math we learned the quadratic formula and how to solve quadratic equations with this formula. I chose this topic because I find using the quadratic formula to be much more consistent and straight forward than ‘complete the square’ method. This skill is important because solving quadratics, especially with the quadratic formula, is a topic that we will build of off in our next units, and the next math courses that I will take.

Lets look at some examples…

Example 1.

This example is a simple quadratic without a leading coefficent larger than one.

Step 1. My first step is to write out the quadratic formula, so I can refer to it in my next step.

Step 2. In my second step, I need to identify the a,b and c values so I know where to plug in my values. In this particular example, the equation is already in general form which makes things much more simple. The is my a value, the x is my b value, and my constant is my c value. This is how it always is.

Step 3. Plug in your a,b,c values into the quadratic equation to solve for x1 and x2. Remeber, if you have two negatives it is equal to a positive so -6 = 6.

Step 4. Expand your values

Step 5. Simplify the inside terms

Step 6. Simplify . 20 breaks down into 4 and 5, and because 4 is a perfect square, it comes out as 2.

Step 7. Since all terms are divisble by 2, we simplify and divide each term by 2. All terms must be divisble by the same value.

Example 2.

In this example we have a quadratic equation with a leading coefficent larger than 1.

Step 1. Convert the equation into general form. The -7x changes to a positive when it is moved to the other side of the equal sign.

Step 2. Identify values of a,b,c. Recall how we solved for these values in example 1.

Step 3. Plug each value into the quadratic formula.

Step 4. Expand the inside terms. BE CAREFUL. 4 X – 1 = -4; -4 X -4 = POSITIVE 16.

Step 5. Add like terms.

Step 6. see if you can simplify the radical, in this case we cannot which gives us our final answer. The +/- sign before the radical indicates there is two different answers. One positive and one negative. A quadratic equation always has 2 answers.

 

Glossary :

Constant :a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

General Form : A formula that contains the degree of variables in decreasing order that = zero

Leading coefficent : the coefficient of the term of highest degree in a given polynomial.

Quadratic Equation : any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.