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Section 8.3

# Section 8.3 - sides 4 Express the trinomial as the square...

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Standard Form for a Quadratic Equation: y = ax 2 + bx + c Solve each of the quadratic equations. Support your results numerically and graphically. 2 2 2 2 1) 0 4 3 3) 3 0 2) 16 64 4) 4 49 x x x x x x = + + + = = - = 2
The Principle of Square Roots 2 For any real number , if , then or - k x k x k x k = = = 3

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Use the square root property to solve. ( 29 2 2 2 2 1) 2 10 3) 16 25 0 2) 7 5 0 4) 2 5 x x x a = + = - + = + = 4
Replace the blanks in each equation with constants to complete the square and form a true equation. ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 1) 8 ___ ___ 2) 18 ___ ___ 3) 3 ___ ___ 5 4) ___ ___ 3 x x x x x x x x x t x x + + = + - + = - + + = + - + = - x + 4 x + 4 x 2 4x 4x 16 5

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Solve a Quadratic Equation by Completing the Square 1) Isolate the terms with variables on one side of the equation, and arrange them in descending order. 2) Divide both sides by the coefficient of x 2 if that coefficient is not 1. 3) Complete the square by taking half of the coefficient of x and adding its square to both

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Unformatted text preview: sides. 4) Express the trinomial as the square of a binomial and simplify the other side. 5) Use the principle of square roots. 6) Solve for x by adding or subtracting on both sides. 6 Solve by completing the square. 2 2 2 2 2 2 1) 8 9 4) 13 4 2) 10 22 5) 2 5 3 3) 5 3 6) Find the x-interecepts: ( ) 4 6 1 x x x x x x x x x x f x x x + = + = --=-- = + + = =--7 Free-Falling Objects If an object is dropped from a height of h feet, its distance d above the ground after t seconds is given by The CN Tower in Toronto, at 1815 ft, is the world’s tallest self-supporting tower on land. How long would it take an object to fall freely from the top? 2 ( ) 16 d t h t =-8...
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Section 8.3 - sides 4 Express the trinomial as the square...

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