Algebra Chapter 10 10 6 Solving Quadratic Equations

Algebra Chapter 10 10. 6 Solving Quadratic Equations by the Quadratic Formula SPI: Find the solution of a quadratic

Your Purpose and Goals for today…. • Are to be able to solve quadratic equations using the quadratic formula. • You all ready know how to solve quadratic equations by completing the square. • You need to know how to use the quadratic formula so you can determine altitude of a rocket or determine how long a ball will stay in the air when thrown from a cliff.

Football…. Suppose a football player kicks a ball and gives it an initial upward velocity of 47 ft/s. The starting height of the football is 3 ft. If no one catches the football, how long will it be in the air?

The Quadratic Formula

Example 1: Solve Substitute values for a, b, and c

Example 2: Solve Substitute values for a, b, and c

Example 3: Solve Substitute values for a, b, and c

Example 4: Solve Substitute values for a, b, and c Round to the nearest hundredth.

Vertical Motion Object Dropped Object Thrown Upward Velocity can be positive (for an object moving up, negative (for an object moving down), or zero for an object that is not moving)

Application problem: Suppose a football player kicks a ball and gives it an initial upward velocity of 47 ft/s. The starting height of the football is 3 ft. If no one catches the football, how long will it be in the air? Vertical motion formula: The football will be in the air for 3 seconds.

Application problem: From the top of a 40 foot cliff, you throw a stone downward at 20 ft/sec into the water below. How long will it take the stone to hit the water? Substitute values The stone will hit the water in approximately 1. 08 seconds.

Application problem: Members of the science club launch a model rocket from ground level with a speed of 96 ft/s. After how many seconds will the rocket have an altitude of 128 ft? Substitute values Subtract 128 from both sides The rocket is 128 ft above the ground after 2 s and after 4 s.

How long will a ball thrown upwards at 20 ft/sec stay in the air if it is thrown from a 100 ft. cliff?

A building contractor…. . Real life example of quadratic equations A building contractor was assigned to build a house of floor area of 1200 sq. ft with an instruction that the length of the floor must be 10 ft more than the width. What would be the floor dimensions of the house?

The contractor sets up an equation as, (l)(w) = 1200 or (w + 10)(w) = 1200 or w 2 + 10 w – 1200 = 0 This is a quadratic equation in real life and the roots are w = -40 and w = 30 The measure of a width can not be negative and hence the practical solution is w = 30 and l = 30 + 10 = 40. Thus the floor dimensions works out to 40 ft x 30 ft

Reflection… • What is the quadratic formula? • What are the specifics that you need to remember when using the quadratic formula to solve a quadratic equation.

Extended Writing… • Tell what method you would use to solve the quadratic equation. Explain your choice or choices.

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