root Zero Solution All of these terms mean the x-intercepts of a function, or the x values that make f(x) = 0.

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Presentation transcript:

root Zero Solution All of these terms mean the x-intercepts of a function, or the x values that make f(x) = 0

 Put the equation into Standard form (ax 2 +bx+c=0)  Replace the 0 with a y. So you will have ◦ y=ax 2 +bx+c  Graph the equation  Look at the x-intercepts to find the solution  Check your solution

 Solve x 2 + 6x + 8 = 0 by graphing.  Graph the related quadratic function  f(x) = x 2 + 6x + 8

 CheckCheck the solutions by substituting each solution into the original equation to see if it is satisfied. (–4) 2 + 6(–4) + 8 = 0 (–2) 2 + 6(–2) + 8 = 0

 Solve x 2 – 4x = –4 by graphing.

 NUMBER THEORY Use a quadratic equation to find two numbers with a sum of 4 and a product of 5. UnderstandLet x = one of the numbers. Then 4 – x = the other number. Solve:Graph the related function.

 Solve –x 2 + 4x – 1 = 0 by graphing.

 Locate the zeros in the function x 2 + 5x – 7 = 0

ROYAL GORGE BRIDGE The highest bridge in the United States is the Royal Gorge Bridge in Colorado. The deck of the bridge is 1053 feet above the river below. Suppose a marble is dropped over the railing from a height of 3 feet above the bridge deck. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula h(t) = –16t 2 + h 0, where t is the time in seconds and h 0 is the initial height above the water in feet.

Solve by Using a Calculator Graph the related function y = –16t using a graphing calculator. Adjust your window so that the x-intercepts are visible. Then locate a right bound and presstwice. ENTER 2nd Use the ZERO feature, [CALC], to find the positive zero of the function, since time cannot be negative. Use the arrow keys to locate a left bound for the zero and press. Solve0 = –16t