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? where x is the variable and a, b & c are constants Examples of Quadratic Equations (a) 5x 2 3x 1 0 is a quadratic equation in quadratic form where a 5, b -3, c -1 (b) 5 + 3t 4.9t 2 0 is a quadratic equation in quadratic form. The general form of a quadratic equation is. 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. Solving Quadratic Equations by Factoring. Step 6: Set each factor equal to 0. And solve the linear equation. Step 4: Write the equation in standard form. 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. Madsen 20 in Global Rating 11 Customer reviews. Substitute the given information to the equation. Unit 4 Solving Quadratic Equations Homework 2 Solving Quadratics By Factoring Answer Key - Viola V. Recognize when the quadratic formula gives complex solutions and write them as ± for real numbers and. Step 3: Determine if there is a special formula needed. Solve quadratic equations by inspection (e.g., for ² 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. 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. Below is a picture representing the graph of y x² + 2x + 1 as well as the solution we found by factoring.
Steps for solving Quadratic application problems:ġ.