Quadratic+Equations


 * QUADRATIC EQUATIONS **

Quadratic Equation: an equation you can write in the standard form--    ax^2+bx+c=0,     where A is not = to zero.
 * 5 KEY TERMS: **
 * parabola
 * axis of symmetry
 * vertex
 * minimum
 * maximum

A quadratic equation is an equation that can be written in the form above. This form is called the __standard form of a quadratic equation.__ A quadratic equation can have two, one,or no real-number solution.

**__ Solving quadratic equation using squareroots __** You can solve equations of the form x^2=a by finding the square roots of each side. Since 6^2=36 and (-6)^2=36 are both true statements, 6 and -6 and both solutions to the equation x^2=36. We write the solution to x^2=36 as +_ square root of 36, or +_ 6.



Example 1 Suppose that one leg of a right triangle is 12 inches while the hypotenuse is

inches.. Find the length of the other leg. Solution Let x be the length of the other leg. Substituting into the Pythagorean theorem we have

. Since the right side is equal to

This equation simplifies to or. This means that x is 4 or -4. Only 4 can be a length of the side of a triangle; so the other leg is 4 inches long. Find two positive consecutive odd integers whose product is 99. Solution Let x be the first integer. Then the next odd integer is x + 2. So we have x(x+2) = 99. To solve this equation first we distribute and then set one side to zero. We have Factoring the left side gives (x + 11)(x - 9) = 0. So the solutions are x = -11 or x = 9. Since we are looking for positive integers, the answers are 9 and 11.

The width of a rectangle is 16 feet less than 3 times the length. If the area is 35 square feet, find the dimensions of the rectangle. Solution Let x be the length because the width is expressed in terms of the length. So the length is 3x - 16. The total area is 35 square feet so we have the equation 35 = x(3x -16). To solve we first distribute: 35 = 3x2 - 16x then set the left side to zero: .  Factoring gives 0 = (3x +5)(x -7). Only the second factor will give a positive solution, so the answer is 7. The dimensions of the rectangle are: Length: 7 feet width: 5 feet.



http://www.mathscareers.org.uk/14_-_16/maths_in_everyday_life/quadratics.cfm </span

http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php </span