Sometimes we are give a problem that includes multiple negative exponents. Methodically simplifying the problem in a step by step approach helps avoid mistakes. Take the following problem:   One option is to take the y^-3 and put it as the denominator. By doing this you can change it to a positive exponent. Now we have ((2x^4)/(y^3))^-1 (see photo below for easy to read equation). Now, let's take the reciprocal of everything inside parentheses so that the exponent of -1 becomes 1....

Take an question such as: Graph 12y-x ≤ 6 on a coordinate plane. First, recall y=mx+b, which describes linear functions. We want to rearrange 12y-x≤6 so that it closely resembles that form. Start by adding x to both sides so that you have: 12y ≤ x+6. Now, divide all terms by 12 so that you get y ≤ (1/12)x+1/2. Now graph the line y=(1/12)x+1/2 as a solid line (because this is "less than or equal to." If it was simply "less than" then we would do a dashed line. Now that you have draw that l...

Break out your compass, ruler and colorful pens. Here's the cliff notes version of constructing a 9 point circle by hand. 1.Draw a scalene triangle and construct midpoints. These are done by putting the sharp end of the compass on a vertex and extending the pencil slightly more than half the estimated distance along that segment of the triangle. Draw an arc and do it the same from the other end of the segment. Repeat for the other two sides. 2. Draw altitudes. Put sharp end of compass at a ver...

Graphing polynomials begins with finding the x-intercepts, or roots, of the function. Take y=(x+1)(x-2)². First set y= to zero and find what values for x satisfies that. If either term equals zero, we know that the product of the two terms will equal zero. So if x=-1 or x=2, y will equal zero. We now can sketch the x-intercepts. Now, let's think about end behavior of the polynomial. Since it is a third degree polynomial (the parent function is x^3), we know that as x becomes more and more negati...