When the equation of your parabola can be written as y = ax^2 + bx + c, the x of the vertex can be found using the formula x = -b / 2a. Simply plug the a and b values from your equation into this formula to find x.  Example: y = -x^2 - 8x - 15 x = -b / 2a = -(-8)/(2*(-1)) = 8/(-2) = -4 x = -4 By plugging a value for x into the equation, you can solve for y. This y value will be the y coordinate of your vertex. Example: y = -x^2 - 8x - 15 = -(-4)^2 - 8(-4) - 15 = -(16) - (-32) - 15 = -16 + 32 - 15 = 1 y = 1 The x and y values you have are the coordinates of your vertex point. Example: (-4, 1)

Summary: Find the x coordinate of the vertex directly. Plug this value into the original equation. Write down your vertex coordinates.


A macro lens will allow you to best capture the detail of the eye. Macro lenses vary in focal length from 50 to 200mm. You can still take a good close-up photo of the eye with a regular lens, but you may not be able to get the eye to fill the entire frame or capture all the detail you want. If you don’t have a macro lens and don’t want to spend the money to get one, try using a close-up filter as an alternative. Many cellphones have a macro mode, which will allow you to take a more detailed photograph of the eye than with your camera’s standard settings. A macro lens attachment for your cellphone will produce even more detailed shots.  You can find a macro lens attachment for your cellphone at most major retailers and electronics stores. If you’re planning to buy a macro lens attachment, make sure you choose one that fits your phone model. Extension tubes fit between the rear mount of the lens and the camera body. Using an extension tube will magnify the eye in your shot, allowing you to capture more intricate details.

Summary: Put a macro lens on your camera. Use a macro mode or macro lens attachment when using a cellphone. Consider adding an extension tube to make the lens focus closer.


Determine the size of the carpet to be cut out, and whether you want to cut a rectangular or circular replacement patch to fill the area in. Rectangular patches can be cut using a utility knife, while circular patches can be cut using a circular carpet cutter. Use a utility knife or a carpet cutting tool to gently cut away the carpet. Apply just enough pressure to cut through both the surface of the carpet and the backing, but not enough to damage the underlying layer of padding. Once the section is completely cut, lift it off the carpet surface.  You may want to save the damaged section in case you need to patch a smaller area that can be cut from this section. Turn a carpet remnant face down and measure a patch for the carpeting, using the measurements obtained earlier as a guideline. Or remove a piece of carpeting from an inconspicuous area, such as the inside of a closet. Mark the lines of the patch with the pencil, and then use a utility knife or carpet cutter to cut out the patch. Carpet patch pads are used to iron on specially made adhesive disks that activate with the help of heat. Your carpet patch pad may be aluminum-sided on the top and contain a previous material on the bottom. Wet your carpet patch pad under water and wring out the excess; the pad should be damp but not dripping. Make sure the adhesive pad is adequately bigger than the patch, specially made for heat-application, and centered for even distribution. Smooth out any wrinkles if necessary Go over the patch with a carpet brush to remove loose fibers. Make sure that the direction of the fibers on the patch matches the direction of the fibers on the carpet. Make sure the patch pad is centered and you know where the patch is underneath. Press down on the iron so that the heat transfers from the patch pad, through the carpet, to the adhesive pad underneath. Remember that the adhesive pad activates when subjected to heat.  You should hear a light sizzle when you touch the iron onto the patch pad. This is the water reacting to the heat, not the carpet burning. If the patch is big, go over different spots the patch with the iron — enough to cover the entire patch. You don't want to fail to activate the head beneath the patch. The glue on the adhesive pad won't fully dry until the carpet is cool. Go over the patch with a carpet brush and remove any loose fibers from the edge of the carpet.

Summary: Measure the damaged area of the carpeting. Remove the damaged section of carpeting. Measure and cut the replacement patch. Wet the carpet patch pad. Slide the adhesive pad underneath the cut-out carpet, centering it. Place the replacement patch onto the adhesive disk. Place the patch pad on top of the patch, aluminum side up. Using an iron set on high, heat the patch pad up for one minute. Remove the iron and patch pad let the area cool.


Even though sandpaper sounds too rough to use on suede, it actually is a great material if you have a gentle hand. Purchase either fine sandpaper (number 000) or use a nail file that you may have at your house. Use soft back-and-forth motions to sand at the gum. Try to avoid directly sanding the surface of the suede. Brush aside any gum that may come off.  Keep in mind that the sanding method will likely affect the suede. A tiny bit of the material may come off as you're sanding. This method is best left after you have tried other methods. It also may be the best method for items like shoes, which are below eye level. If your suede item is something that people will be looking at up close, keep in mind that the material will be affected. Sanding suede with a brush or emery board can affect the nap, or texture of the suede. After sanding, take a toothbrush, nail brush or suede brush and gently brush the nap of the suede, going in one direction. Brushing the suede can also brush away the gum removed during sanding.
Summary: Purchase sandpaper or a nail file. Gently move the sandpaper or nail file over the gum remains. Brush with a suede brush.