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Solve Quadratic Equations by the Quadratic Formula

Goals • Solve quadratic equations using the quadratic
formula.

Your Notes	VOCABULARY Quadratic formula A formula that gives the solutions of any quadratic equation in standard form
	THE QUADRATIC FORMULA The roots of the polynomial and the solutions of the quadratic equation are when a ≠ 0 and
	Example 1 Multiple Choice Practice
	Which is one of the solutions to the equation
	Solution
		Quadratic formula
		Substitute values in the quadratic formula: a = 2 , b = -3 , and c = -5 .
		Simplify.
		Simplify the square root.
	One solution is -1. The correct answer is B
Your Notes	Example 2 Use the quadratic formula
	Crabbing A crabbing net is thrown from a bridge, which is 35 feet above the water. If the net's initial velocity is 10 feet per second, how long will it take the net to hit the water? Solution The net's initial velocity is v = 10 feet per second and the net's initial height is s = 35 feet. The net will hit the water when the height is 0 feet.
		Vertical motion model
		Substitute for h, v, and s.
		Substitute values in the quadratic formula: a = -16 , b= 10 , and c = 35 .
		Simplify.
	The solutions are and
	Because time cannot be a negative number, disregard the negative solution.	So, the net will hit the water in about 1.82 seconds.

	Guided Practice Complete the following exercises.
	1. Use the quadratic formula to solve and
	2. In Example 2, suppose the net was thrown with an initial velocity of 5 feet per second from a height of 20 feet. How long would it take the net to hit the water? about 1.29 seconds
Your Notes	METHODS FOR SOLVING QUADRATIC EQUATIONS
	Methods	When to Use
	Factoring	Use when a quadratic equation can be factored easily.
	Graphing	Use when approximate solutions are adequate.
	Finding	Use when solving an equation that can
	square roots	be written in the form x² = d .
	Completing	Can be used for any quadratic equation
	the square	Can be used for any quadratic equation the square but is simplest to apply when a = 1 and b is an even number.
	Quadratic	Can be used for any quadratic equation.
	formula
	Example 3 Choose a solution method
	Tell what method(s) you would use to solve the quadratic equation. Explain your choice(s). Solution a. The quadratic equation cannot be factored easily and completing the square would result in many fractions . So, the equation can be solved using the quadratic formula . b. The quadratic equation can be solved using square roots because the equation can be written in the form x² = d.
	Guided Practice Complete the following exercise.
Homework	3. Tell what method(s) you would use to solve . Explain your choices(s). factoring: the expression can be factored easily; completing the square: the equation is of the form where a= 1 and b is an even number.

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Solve Quadratic Equations by the Quadratic Formula