Chapter 5: Exercises with Solutions

Section 5.4The Quadratic FormulaTo find the x-intercepts algebraically, set −x 2 − 8x − 9 = 0 and use the quadraticformula with a = −1, b = −8 and c = −9:x = −b ± √ b 2 − 4ac2a= 8 ± √ (−8) 2 − 4(−1)(−9)2(−1)= 8 ± √ 64 − 36−2= 8 ± √ 28−2So the x-intercepts are ((8 − √ 28)/(−2), 0) and ((8 + √ 28)/(−2), 0). These are approximatedon your calculator in (a) and (b).(a)(b)Lastly, to find the y-intercept, set x = 0 in the equation and solve for y:f(x) = −x 2 − 8x − 9f(0) = −(0) 2 − 8(0) − 9f(0) = −9So the y-intercept is (0, −9).Finally, put this all together to make the graph.x=−420y(−4,7)((8+ √ 28)/(−2),0) ((8− √ 28)/(−2),0)x10(−8,−9)(0,−9)f(x)=−(x+4) 2 +7Version: Fall 2007