To factor the expression x^2+7x+12, we must first determine the factors of c, in this case 12. Now, let’s solve for the x-intercepts by factoring. To start, let’s try solving the equation: But no need to worry, we include more complex examples in the next section. We simply must determine the values of r_1 and r_2. In these cases, solving quadratic equations by factoring is a bit simpler because we know factored form, y=(x-r_1)(x-r_2), will also have no coefficients in front of x. If a=1, then no coefficient appears in front of x^2. Remember, the standard form of a quadratic is:įor more information about forms of quadratics, check out our article on the different forms of quadratics. For our purpose, a simple quadratic means a quadratic where a=1. The x-intercepts can also be referred to as zeros, roots, or solutions. When you are asked to “solve a quadratic equation”, you are determining the x-intercepts. Return to the Table of Contents Factoring Quadratic Equations Examplesīefore things get too complicated, let’s begin by solving a simple quadratic equation. …we are simply saying that when we multiply (x-r_1) and (x-r_2), we will get the product ax^2+bx+x. Likewise, when we factor the standard from of a quadratic equation: Factors are terms that, when multiplied together, produce the original number or expression.Factoring a number or expression means breaking it into separate factors.There are other ways to factor 12, as well, such as using the factors 4 and 3 instead. The numbers 6 and 2 are factors of 12 because multiplying 6 and 2 gives the product of 12. Solving a Quadratic Equation Using Completing the Squareīefore we dig deep into factoring quadratic equations, let’s remember what factors are by looking at numerical examples.
Determine a Quadratic Equation Given Its Roots.Solving Quadratic Equations by Factoring: World Problems.Factoring Trinomial with The Box Method.Video Examples of Factoring Quadratic Equation.Solving Quadratic Equations with the “AC Method”.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.