Before approaching this topic, it’s important that you’re able to factor fully. We’ll consider what it actually means graphically to solve a quadratic equation and how this process looks for a variety of equations. Solve a Quadratic Equation by COMPLETING THE SQUARE. In this video, we’ll learn how to solve quadratic equations by factoring, sometimes called factorizing. To determine when the height of the ball is 336 feet. Put each linear factor equal to (0) (to apply the zero product rule). Factorize (ax2+bx+c) into two linear factors. Make the given equation free from fractions and radicals and put it into the standard form (ax2+bx+c0.) Step 2. 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? Method of Solving a Quadratic Equation by Factorizing: Step 1. 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. To solve quadratic equations by factoring, we must make use of the zero-factor property. Step 6: Set each factor equal to 0. And solve the linear equation. Learn how to use the Zero Product Property to solve quadratic equations by factoring. ![]() Step 4: Write the equation in standard form. So we must be sure to start with the quadratic equation in standard form, a x 2 + b x + c 0 a x 2 + b x. In order to use the Zero Product Property, the quadratic equation must be factored, with zero on one side. Substitute the given information to the equation. Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations: x + 2 0 or x + 3 0. Each of the equations we have solved in this section so far had one side in factored form. 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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