Watch Video on The Quadratic Formula - Algebra Help
Wednesday, August 26th, 2009
Access full lesson containing this video at: http://www.yourteacher.com/algebra2/thequadraticformula.php Students learn to solve quadratic equations in the form ax^2 + bx + c = 0 using the quadratic formula, which states that x = -b plus or minus the square root of b^2 — 4ac over 2a. For example, to solve the equation x^2 — 3x — 8 = 0, since a = 1, b = -3, and c = -8, the quadratic formula states that x = 3 plus or minus the square root of (-3)^2 — 4(1)(-8) over 2(1). Simplifying on the right side of the equation, x = 3 plus or minus the square root of 9 + 32 over 2, or x = 3 plus or minus the square root of 41 over 2, which is the final answer. Note that students also learn to derive the quadratic formula using completing the square in the first example problem in this lesson.
Duration : 0:3:39
Access full lesson containing this video at: http://www.yourteacher.com/algebra1/decimalequations.php Students learn that if one or more decimals appear in an equation, the first step is to get rid of the decimals by multiplying both sides of the equation by the appropriate power of 10. For example, if the equation reads x + .7 = .9x — 3, since both decimals are taken to the tenths place, the decimals can be removed by multiplying both sides of the equation by 10, to get 10x + 7 = 9x - 30. Note that all solutions in this lesson are integers.
Access full lesson containing this video at: http://www.yourteacher.com/prealgebra/multiplicationequations.php Students learn to solve one-step multiplication equations. For example, to solve 7x = 28, divide both sides of the equation by 7, to get x = 4. Next, check the solution by substituting a 4 back into the original equation, to get 7(4) = 28, which is a true statement, so the solution checks.
Access full lesson containing this video at: http://www.yourteacher.com/geometry/factoringquadraticequations.php Students learn that the first step in solving polynomial equations is to set the given equation equal to zero, the next step is to factor, and the final step is to set each of the resulting factors equal to zero and solve each equation. This process usually yields more than one solution, so the answer can be written as a solution set. Some of the problems involve factoring a trinomial into two binomials, and some of the problems involve factoring a binomial as the difference of two squares.
Access full lesson containing this video at: http://www.yourteacher.com/prealgebra/subtractionequations.php Students learn to solve one-step subtraction equations. For example, to solve z - 3 = 16, add 3 to both sides of the equation, to get z = 19. Next, check the solution by substituting a 19 back into the original equation, to get (19) — 3 = 16, which is a true statement, so the solution checks.