Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503

Quadratic Equations Standard form: ax 2 + bx + c = 0

Find the square root of numbers

1. 2.

Find the square root of numbers 1. 2.

Find the square root of numbers 1.

Key Concepts When x 2 = d If d > 0, then x 2 = d has two solutions example: If d = 0, then x 2 = d has one solution example: If d < 0, then x 2 = d has no real solution example:

Find the square root of numbers 1. 2.

Find the square root of numbers 1.2.

Find the square root of numbers 1.2.

Find the square root of numbers 1.2.

Real Life: Equation of a falling object When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model. h is the ending height in feet above the ground t is the number of seconds the object has been falling s is the starting height from which the object was dropped

Application Sarah is going to drop a water balloon from a height of 144 feet. To the nearest tenth of a second, about how long will it take for the balloon to hit the ground? Assume there is no air resistance.

The question asks to find the time it takes for the container to hit the ground. Initial height (s) = 144 feet Height when its ground (h) = 0 feet Time it takes to hit ground (t) = unknown

Substitute 3 sec.

Substitute 4.24 sec.

Find the square root of numbers 1.2.

Application An engineering student is in an “egg dropping contest.” The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground? Assume there is no air resistance.

The question asks to find the time it takes for the container to hit the ground. Initial height (s) = 32 feet Height when its ground (h) = 0 feet Time it takes to hit ground (t) = unknown

Substitute Approximately 1.4 sec.

Evaluate a Radical Expression

Perfect Squares: Numbers whose square roots are integers or quotients of integers.

What is a square root? If a number square (b 2 ) = another number (a), then b is the square root of a. Example: If 3 2 = 9, then 3 is the square root of 9

Quadratic Equations Standard form: ax 2 + bx + c = 0 a is the leading coefficient and cannot be equal to zero. If the value of b were equal to zero, the equation becomes ax 2 + c = 0. We can solve equations is this form by taking the square root of both sides.

Some basics… All positive numbers have two square roots The 1 st is a positive square root, or principal square root. The 2 nd is a negative square root Square roots are written with a radical symbol You can show both square roots by using the “plus-minus” symbol ±