Factor: 12x2 - 17x 6
Practice factoring a trinomial with a negative middle term: 12x2 - 17x 6.
Finding Distance on a Graph Using the Pythagorean Theorem and the Distance Formula
The Pythagorean Theorem can be used to solve a distance problem on the coordinate plane. The same problem is also solved using the distance formula.
Solve: 3x(x - 2) = 14
The equation 3x(x - 2) = 14 is solved using the quadratic formula.
Quadratic Equations in Standard Form
The standard form for a quadratic equation is ax2 bx = 0. It is not always clear whether an equation is a quadratic equation until it is simplified. Any equation that can be written in stand form is a quadratic equation.
Practical Problem: How Much Land to Buy
A practical problem involving the purchase of land is presented. The available information is organized into a table, an equation is written, then solved using the least common denominator to get a quadratic equation, and the solution checked.
Solve: 9x2 - 24x = -16
Practice solving an equation using the quadratic formula: 9x2 - 24x = -16.
Finding the Length of the Third Side of a Right Triangle
The Pythagorean Theorem can also be used to determine the length of the hypotenuse given the length of the legs, or the length of a leg given the length of the hypotenuse and the other leg. The formula is demonstrated for both purposes.
Factor: 2k2 - 18k - 72
Factoring a quadratic trinomial with a leading coefficient greater than one.
Practical Problem: Machines Working at Different Speeds
The procedure for developing an equation to solve a practical work problem involving machines working at different speeds is detailed. The unknown is identified and an equation is written, solved, and checked.
Practical Problem: Pricing a Product and Maximizing Profit
Using a quadratic equation with two variables to solve a practical problem involving product pricing.