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4-2 Solving Equations by Graphing

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

Possible solutions

Example 1 Solve x2 + 6x + 8 = 0 by using the given graph.

Steps to Solve by Graphing Make sure the f(x) or y is isolated Graph the equation Look at the x-intercepts to find the solution Use graph Use table Use CALC

Solve x2 – 4x = –4 by graphing. Example 3 Solve x2 – 4x = –4 by graphing.

Example 4 Solve –x2 + 4x – 1 = 0 by graphing. Use the ZERO feature, (2nd [CALC]), to find the zeros of the function. Enter the left bound for the zero and press [ENTER ]. Enter the right bound and press [ENTER] twice.

Locate the zeros in the function 2(x- 3) 2 – 9 = 0 Example 5 Locate the zeros in the function 2(x- 3) 2 – 9 = 0

Example 6 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 + h0, where t is the time in seconds and h0 is the initial height above the water in feet.

Solve by Using a Calculator Solve 0 = –16t 2 + 1056. Graph the related function y = –16t 2 + 1056 using a graphing calculator. Adjust your window so that the x-intercepts are visible.

Write your name with 4 X’s under it Mr. Van Vleet X X X X

𝑥 2 −11𝑥+19=−5 𝑥 2 −10𝑥+22=−2 7 𝑥 2 −14𝑥=−7 3 𝑥 2 −16𝑥−12=0 Solve each equation 𝑥 2 −11𝑥+19=−5 𝑥 2 −10𝑥+22=−2 7 𝑥 2 −14𝑥=−7 3 𝑥 2 −16𝑥−12=0 7 𝑥 2 +2𝑥=0

What is the y-intercept of the following function 𝑓 𝑥 = 𝑥−2 2 +5 𝑦=5 𝑥 2 −7𝑥+2 𝑦=4−2 𝑥 2 +7𝑥

How has the graph of 𝑦= 𝑥 2 been shifted to get 𝑦= 𝑥−1 2 +4 ?

What is the domain and range of the quadratic function graphed to the right?

What are the roots/zeros of the following function? 𝑦=(𝑥+4)(𝑥−7)

Homework Page 233: 15-19, 23-26, 38-40