Q: Write your quadratic function in general form, f(x)=ax2+bx+c{\displaystyle f(x)=ax^{2}+bx+c}. If necessary, you may need to combine like terms and rearrange to get the proper form. Begin with the sample function f(x)=2x24x+1{\displaystyle f(x)=2x^{2}-4x+1}. Using basic first-year calculus, you can find the first derivative of the general quadratic function to be f(x)=2ax+b{\displaystyle f^{\prime }(x)=2ax+b}. For the sample function f(x)=2x24x+1{\displaystyle f(x)=2x^{2}-4x+1}, find the derivative as: f(x)=4x4{\displaystyle f^{\prime }(x)=4x-4} Recall that derivative of a function tells you the slope of the function at that selected point. The minimum or maximum of a function occurs when the slope is zero. Therefore, to find where the minimum or maximum occurs, set the derivative equal to zero. Continue with the sample problem from above: f(x)=4x4{\displaystyle f^{\prime }(x)=4x-4} 0=4x4{\displaystyle 0=4x-4} Use basic rules of algebra to rearrange the function and solve the value for x, when the derivative equals zero. This solution will tell you the x-coordinate of the vertex of the function, which is where the maximum or minimum will occur. 0=4x4{\displaystyle 0=4x-4} 4=4x{\displaystyle 4=4x} 1=x{\displaystyle 1=x} The minimum or maximum value of the function will be the value for f(x){\displaystyle f(x)} at the selected x{\displaystyle x} position. Insert your value of x{\displaystyle x} into the original function and solve to find the minimum or maximum. For the function f(x)=2x24x+1{\displaystyle f(x)=2x^{2}-4x+1} at x=1{\displaystyle x=1}, f(1)=2(1)24(1)+1{\displaystyle f(1)=2(1)^{2}-4(1)+1} f(1)=24+1{\displaystyle f(1)=2-4+1} f(1)=1{\displaystyle f(1)=-1} The solution gives you the vertex of the maximum or minimum point. For this sample function, f(x)=2x24x+1{\displaystyle f(x)=2x^{2}-4x+1}, the vertex occurs at (1,1){\displaystyle (1,-1)}. The coefficient a{\displaystyle a} is positive, so the function opens upward. Therefore, the minimum value of the function is the y-coordinate of the vertex, which is 1{\displaystyle -1}.
A: Start with the general form. Use the power rule to find the first derivative. Set the derivative equal to zero. Solve for x. Insert the solved value of x into the original function. Report your solution.

Q: This method of removing mildew from fabric uses a borax soak to pre-treat your laundry before washing it. To start, make a mixture of borax and water with a ratio of about 1 cup (204 grams) of borax per 1 quart (1 liter) of water, then add more borax and water if needed. Use a clean bucket or tub to hold your mixture. Borax is a cheap, readily available laundry additive. You can find it in more grocery stores alongside the other laundry detergents. If you can't find any borax, use an ordinary detergent or non-chlorine bleach that's safe for your fabric. In general, hot water cleans stains (including mildew) better than cold water, making it a good, default choice for laundry. However, not all fabrics may be safe for hot water cleaning. If your fabric can't be washed in hot water, allow the mixture to cool first. Don't mix borax into cold water; it will most likely clump up. Use a stick or spoon to agitate the fabric. Make sure all ofnot just the mildewed portiongets a chance to absorb the solution. If your fabric won't stay under the solution, you can weigh it down with a jar. Once your fabric has had a chance to soak, remove it from the solution and gently squeeze it over a sink or drain to remove the excess water. Next, apply a small dot of normal detergent to the mildew stain and use a soft-bristled brush (such as an old toothbrush) to scrub the stain away. It's a good idea to scrub the stain from the opposite side of the fabric when possible. Doing this can work the stain away from the fabric, rather than driving the stain further into it. It also reduces the appearance of wear-and-tear on the article. Your fabric is now pre-treated and ready for the wash. In general, hot water and a long, high-powered wash will be most effective at cleaning your fabric. However, these conditions can damage some fabrics, so obey all instructions on your item's care label. Unless your item is seriously soiled, you can safely do an entire load of laundry at this point without fear of harming the other clothes, so don't be afraid to toss in similar fabrics with your soiled item. For whites, you may add bleach to the wash. For colored fabrics, use only colorfast bleaches or similar detergents that won't cause them to bleed. When your wash is done, hang the clothes up on a clothesline to dry. Don't put them into a dryer, as heat will set in the stainsincluding mildew. Once the clothes are dry, inspect them; if you notice any mildew, repeat the cleaning process. Try to dry your clothes in the sun. This will help further kill any mildew. If you must use a clothes dryer, use the no-heat setting.
A:
Dissolve 2 cups (408 grams) of borax in 2 quarts (2 liters) of warm or hot water. Add your mildew-stained fabric into the solution and let it soak for 5 to 10 minutes. Gently brush your normal detergent into the fabric. Wash on the highest setting allowed for your fabric. Air-dry the item, and repeat the cleaning process if necessary.