Lesson 10-2 Solving Quadratic Equations by Graphing

Definitions Standard Form - y = ax 2 + bx + c, where a  0. Roots - The solutions of a quadratic equation, which can be found by finding the x-intercepts or zeros of the related quadratic function. Symbol used to express empty set or no real solutions.

Two roots -3 and 3 Types of roots. (x+3)(x-3)

Double root of 2 Types of roots. (x-2) 2

No real roots Types of roots.

Rational roots -2  x  -1 and 1  x  2

Solve x 2 + 6x -7 = 0 by graphing. Find the roots. xy

Solve x 2 - 6x -9 by graphing. xy

Solve x 2 +2x +3=0 by graphing. xy

xy Solve x 2 -4x +2 = 0 by graphing. For integral roots, state the consecutive integers the root lies between.

Shelly built a model rocket for her science project. The equation y = -16t t models the flight of the rocket, launched from ground level at a velocity of 250 feet per second, where y is the height of the rocket in feet after t seconds. For how many seconds was Shelly’s rocket in the air? xy Y = -16t t