Solve a Quadratic Equation by COMPLETING THE SQUARE. Solve quadratic equations by factoring, completing the square, taking the square root or using the quadratic formula. To do this, we begin with a general quadratic equation in standard form and solve for (x) by completing the square. To determine when the height of the ball is 336 feet. In this section, we will develop a formula that gives the solutions to any quadratic equation in standard form. 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. When a quadratic equation is written in standard form so that the values (a, b), and (c) are readily determined, the equation can be solved using the quadratic formula. Step 3: Determine if there is a special formula needed. Set the equation equal to zero, that is, get all the nonzero terms on one side of the equal sign and 0 on the other. Theyve given me the equation already in that form. To solve quadratic equations by factoring, we must make use of the zero-factor property. The Quadratic Formula requires that I have the quadratic expression on one side of the 'equals' sign, with 'zero' on the other side. Step 1: Draw and label a picture if necessary. Use the Quadratic Formula to solve x 2 4x 8 0 Affiliate. Now solve a few similar equations on your own. We do this exactly as we would isolate the x term in a linear equation. 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. For example, to solve the equation 2 x 2 + 3 131 we should first isolate x 2. 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. If a quadratic equation can be solved by factoring or by extracting square roots you should use that method. However, it is sometimes not the most efficient method. Determine if there is a special formula needed. The quadratic formula can solve any quadratic equation. Steps for solving Quadratic application problems:ġ.
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