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**Solving Quadratic Equations by Finding Square Roots**

This lesson comes from chapter 9.1 from your textbook, page 503

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What is a square root? If a number square (b2) = another number (a), then b is the square root of a. Example: If 32 = 9, then 3 is the square root of 9

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**Some basics… All positive numbers have two square roots**

The 1st is a positive square root, or principal square root. The 2nd 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 ±

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**Find the square root of numbers**

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

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**Evaluate a Radical Expression**

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**Quadratic Equations Standard form: ax2 + 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 ax2 + c = 0. We can solve equations is this form by taking the square root of both sides.

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**Key Concepts When x2 = d If d > 0, then x2 = d has two solutions**

If d = 0, then x2 = d has one solution If d < 0, then x2 = d has no real solution

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**Solving quadratics Solve each equation.**

a. x2=4 b. x2=5 c. x2=0 d. x2=-1 x2=4 has two solutions, x = 2, x = -2 x2=5 has two solutions, x =√5, x =- √5 x2=0 has one solution, x = 0 x2=-1 has no real solution

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**Solve by rewriting equation**

Solve 3x2 – 48 = 0 3x2 – = 3x2 = 48 3x2 / 3 = 48 / 3 x2 = 16 After taking square root of both sides, x = ± 4

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**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 height in feet above the ground t is the number of seconds the object has been falling s is the initial height from which the object was dropped

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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.

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**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

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Substitute 0 = -16t2 + 32 = -16t – 32 -32 = -16t2 -32 / -16 = -16t2 / -16 2 = t2 t = √2 seconds or approx. 1.4 seconds

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