Let's say the formula you're working with is the following: f(x) = 3x2 + 6x -2. This means that when you place any x into the equation, you'll get your y value. This is the function of a parabola. If you're working with a straight line or any function with a polynomial of an odd number, such as f(x) = 6x3+2x + 7, you can skip this step. But if you're working with a parabola, or any equation where the x-coordinate is squared or raised to an even power, you'll need to plot the vertex. To do this, just use the formula -b/2a to get the x coordinate of the function 3x2 + 6x -2, where 3 = a, 6 = b, and -2 = c. In this case -b is -6, and 2a is 6, so the x-coordinate is -6/6, or -1.  Now, plug -1 into the function to get the y-coordinate. f(-1) = 3(-1)2 + 6(-1) -2 = 3 - 6 -2 = -5. The vertex is (-1,-5). Graph it by drawing a point where the x coordinate is -1 and where the y-coordinate is -5. It should be in the third quadrant of the graph. To get a sense of the function, you should plug in a few other x-coordinates so you can get a sense of what the function looks like before you start to look for the range. Since it's a parabola and the x2 coordinate is positive, it'll be pointing upward. But just to cover your bases, let's plug in some x-coordinates to see what y coordinates they yield:  f(-2) = 3(-2)2 + 6(-2) -2 = -2. One point on the graph is (-2, -2) f(0) = 3(0)2 + 6(0) -2 = -2. Another point on the graph is (0,-2) f(1) = 3(1)2 + 6(1) -2 = 7. A third point on the graph is (1, 7). Now, look at the y-coordinates on the graph and find the lowest point at which the graph touches a y-coordinate. In this case, the lowest y-coordinate is at the vertex, -5, and the graph extends infinitely above this point. This means that the range of the function is y = all real numbers ≥ -5.
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One-sentence summary -- Write down the formula. Find the vertex of the function if it's quadratic. Find a few other points in the function. Find the range on the graph.


Most people have some sort of bias. That means that you likely believe in some stereotypes, whether you know if or not. You can take an online test to see what your personal biases are. Harvard University offers a variety of free, online tests.  Log into www.implicit.harvard.edu and click “Take Test.” If you don't have an account, you can register for one. Choose a test related to gender such as “Gender-Career.” Complete the questions and read your results. You can also take other tests to help yourself gain a better understanding of bias. Your results will likely indicate that you have an “Automatic Association for Male with Career and Female for Family.” Your automatic association will be described as “slight”, “moderate”, “strong”, or “no bias.” This will let you know how entrenched your ideas are.  If you have bias, try to make “structured decisions.” When you face a decision, evaluate all options and weigh the benefits. This will help you eliminate bias. For example, if you need to promote someone, make a list of each candidate's strengths. This will help keep you from unknowingly defaulting to a particular gender. You could also try “blind auditions.” If you’re hiring musicians, for example, have them perform behind a curtain so that you can’t see their gender. You can adapt this type of strategy for your own life. Male stereotypes are especially common when it comes to jobs. For example, careers in the sciences are still predominantly male, while careers in education are strongly female. Don’t let yourself feel pressured to conform to career stereotypes. Identify what job you want and go for it.  Base your decision on your own skills, your own preferences, and your own goals. For example, if you are a male and want to become a nurse, don’t worry about it being considered a “female” job. There are also lots of gender stereotypes when it comes to hobbies and activities. To break away from these stereotypes, push yourself outside of your comfort zone. Try something that you previously considered a “female” activity. For example, take a cooking class or buy yourself a beautiful bouquet of flowers. As a male, you might feel pressure to participate in traditional male leisure activities. Sports is the best example of this. Many people will assume that because you are male, you are really into sports. Don’t be afraid to spend time doing what you really enjoy.  You could say, “No, I’m not available to watch football on Sundays this season. I’m going to take an art class on Sundays.” Of course, if you genuinely like sports, go for it! It's okay to enjoy things that are "typical."
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One-sentence summary -- Complete a bias test. Take steps to correct those biases. Find a fulfilling job. Embrace new experiences. Spend time doing what you enjoy.


. Mixed numbers are whole numbers with fractions. To make it easier to subtract, turn the whole numbers into fractions. This will mean that the numerator will be larger than the denominator. For example, 2 3/4 - 1 1/7 will become 11/4 - 8/7. Find the lowest common multiple of both denominators so you can make a like denominator for the fractions. For example, if you're doing 11/4 - 8/7, list all the multiples of 4 and 7 to find 28. Since the multiples of 4 include 4, 8, 12, 16, 20, 24, 28 and the multiples of 7 include 7, 14, 21, and 28, 28 is the lowest number they have in common. You'll need to make denominators become the lowest common multiple. To do this, multiply the entire fraction. For example, to make the denominator for 11/4 become 28, multiply the fraction by 7. The fraction will become 77/28. If you've changed the denominator for 1 of the fractions in your problem, you'll need to adjust the other fractions so their ratios are still equal to the original problem. For example, if you've adjusted 11/4 to become 77/28, multiply the 8/7 by 4 to get 32/28. The problem 11/4 - 8/7 becomes 77/28 - 32/28. If the denominators were the same to begin with or you've made equivalent fractions, you can now subtract the numerators. Write the answer and place it over the denominator. Remember not to subtract the denominator. For example, 77/28 - 32/28 = 45/28. You'll probably need to change the answer into a mixed number. Start by dividing the numerator by the denominator to get a whole number. Then write how many parts you have left. This number will be the numerator. Place the numerator over the same denominator. Reduce this fraction if you can. For example, 45/28 becomes 1 17/28 because 28 goes into 45 1 time and has 17 parts of 28 left over.
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One-sentence summary --
Change the mixed numbers into improper fractions Find a common denominator if necessary. Make equivalent fractions if you have to change the denominators. Adjust all of the fractions in the problem to make them equivalent. Subtract the numerators and keep the denominator the same. Simplify the answer.