Find the y-intercepts by substituting 0 for x and solving for y. x 2( y 2)2 4 0 2( y 2)2 4 Substitute 0 for x. 4 2( y 2)2 Subtract 4. 2 ( y 2)2 Divide by 2. 12 y 2 Square root property 2 12 y Add 2. The y-intercepts are (0, 2 12) and (0, 2 12). Use the axis of symmetry to locate the point (4, 4) on the graph. The domain is (q, 4; the range is (q, q). YOU TRY 4 Graph x (y 1)2 3. Find the x- and y-intercepts and the domain and range. Procedure Graphing Parabolas from the Form x ay2 by c We can use two methods to graph x ay2 by c. Method 1: Rewrite x ay2 by c in the form x a(y k)2 h by completing the square. Method 2: Use the formula y b 2a to fi nd the y-coordinate of the vertex. Find the x-coordinate by substituting the y-value into the equation x ay2 by c. 5 Rewrite x ay2 by c as x a(y k)2 h by Completing the Square Rewrite x 2y2 4y 8 in the form x a( y k)2 h by completing the square. Solution To complete the square, follow the same procedure used for quadratic functions. (This is outlined on p. 659 in Section 10.5.) Step 1: Divide the equation by 2 so that the coeffi cient of y2 is 1. x 2 y2 2y 4 Step 2: Separate the constant from the variable terms using parentheses. x 2 (y2 2y) 4 Step 3: Complete the square for the quantity in parentheses. Add 1 inside the parentheses, and subtract 1 from the 4. x 2 ( y2 2y 1) 4 1 x 2 ( y2 2y 1) 3 Notice how this compares to the procedure for graphing f(x) ax2 bx c. EXAMPLE 5 674 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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