536 Chapter 9Solving Quadratic EquationsSolving Quadratic Equations Using the Quadratic Formula (pp. 515–524)9.5Solve −3x2 x = −8 using the Quadratic Formula. 3x2 + x 8 Write the equation. 3x2 + x + 8 0 Write in standard form. x b ± √— b2 4ac ——
2a Quadratic Formula x 1 ± √—— 12 4(3)(8)
—— 2(3) Substitute 3 for a, 1 for b, and 8 for c. x 1 ± √— 97
— 6 Simplify. So, the solutions are x 1 + √— 97
— 6 ≈ 1.5 and x 1 √— 97
— 6 ≈ 1.8.Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, ifnecessary. 27. x2 + 2x 15 0 28. 2x2 x + 8 16 29. 5x2 + 10x 5Find the number of x-intercepts of the graph of the function. 30. y x2 + 6x 9 31. y 2x2 + 4x + 8 32. y 1 — 2 x2 + 2xSolving Nonlinear Systems of Equations (pp. 525–532)9.6Solve the system by substitution. y = x2 − 5 Equation 1y = −x 1 Equation 2Step 1 The equations are already solved for y.Step 2Substitute x + 1 for y in Equation 1 and solve for x.x + 1 x2 5 Substitute x + 1 for y in Equation 1.1 x2 + x 5Add x to each side.0 x2 + x 6 Subtract 1 from each side.0 (x + 3)(x 2) Factor the polynomial. x + 3 0 or x 2 0Zero-Product Property x 3 or x 2Solve for x.Step 3Substitute 3 and 2 for x in Equation 2 and solve for y. y (3) + 1 Substitute for x in Equation 2. y 2 + 1 4 Simplify. 1 So, the solutions are (3, 4) and (2, 1).Solve the system using any method. 33. y x2 2x 4 34. y x2 9 35. y 2 ( 1 — 2 ) x 5y 5 y 2x + 5 y x2 x + 4