![]() Use the sign when taking the square root of the constant term. Take the square root of each side of the equation.This technique, which involves taking the square root of both sides of an equation, should be used when an equation contains one squared term and constants. ![]() This is especially true when the leading coefficient a is not equal to 1. I tell my students to apply the “10 second rule” when trying to factor the expression – if you cannot factor the expression quickly (10 seconds or less) then you should move on to another technique. In most cases, if you can factor the expression you can determine the solutions by inspection, which speeds up the process. If you can factor the quadratic expression, determining the solutions is quite easy. This should be the first tool to try when solving a quadratic equations that is in standard form. In this blog I’ll go over some of the other techniques and help you to determine when to use them. But, depending on the equation, there are often more efficient techniques. While learning to solve quadratic equations, some students decide to always use the quadratic formula because they can use it for any equation. Solving Quadratic Equations – Choosing an Efficient Technique Solve a Quadratic Equation by COMPLETING THE SQUARE. To determine when the height of the ball is 336 feet. The distance along the ground from the bottom of the pole to the end of the wire is 4 feet greater than the height where the wire is attached to the pole. How far up the pole does the guy wire reach?Įxample 4: You throw a ball straight up from a rooftop 384 feet high with an initial speed of 3 feet per second. The functionĭescribes the height of the ball above the ground, s (t), in feet, t seconds after you threw it. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Eliminate any unreasonable answers.Įxample 2: Each side of a square is lengthened by 7 inches. The area of this new larger square is 81 square inches. Find the length of a side of the original square.Įxample 3: A guy wire is attached to a tree to help it grow straight. The length of the wire is 2 feet greater than the distance from the base of the tree to the stake. The height of the wooden part of the tree is 1 foot greater than the distance from the base of the tree to the stake.Įxample 5: A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. Step 6: Set each factor equal to 0. And solve the linear equation. Step 4: Write the equation in standard form. Substitute the given information to the equation. Step 3: Determine if there is a special formula needed. Step 1: Draw and label a picture if necessary. Įxample 1: A vacant rectangular lot is being turned into a community vegetable garden measuring 8 meters by 12 meters. A path of uniform width is to surround garden. If the area of the lot is 140 square meters, find the width of the path surrounding the garden. of carpet.)Īrea of a rectangle and Landscaping/border/frame problems. Set each factor equal to 0. And solve the linear equation. Substitute the given information into the equation.Ħ. Determine if there is a special formula needed. Steps for solving Quadratic application problems:ġ.
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