Solutions to Odd-Numbered Exercises

1. When written in that form, the vertex can be easily identified.

3. If $a=0$ then the function becomes a linear function.

5. If possible, we can use factoring. Otherwise, we can use the quadratic formula.

7. $f\left(x\right)={\left(x+1\right)}^{2}-2$, Vertex $\left(-1,-4\right)$

9. $f\left(x\right)={\left(x+\frac{5}{2}\right)}^{2}-\frac{33}{4}$, Vertex $\left(-\frac{5}{2},-\frac{33}{4}\right)$

11. $f\left(x\right)=3{\left(x - 1\right)}^{2}-12$, Vertex $\left(1,-12\right)$

13. $f\left(x\right)=3{\left(x-\frac{5}{6}\right)}^{2}-\frac{37}{12}$, Vertex $\left(\frac{5}{6},-\frac{37}{12}\right)$

15. Minimum is $-\frac{17}{2}$ and occurs at $\frac{5}{2}$. Axis of symmetry is $x=\frac{5}{2}$.

17. Minimum is $-\frac{17}{16}$ and occurs at $-\frac{1}{8}$. Axis of symmetry is $x=-\frac{1}{8}$.

19. Minimum is $-\frac{7}{2}$ and occurs at –3. Axis of symmetry is $x=-3$.

21. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[2,\infty \right)$.

23. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-5,\infty \right)$.

25. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-12,\infty \right)$.

27. Domain is $\left(-\infty ,\infty \right)$. Range is $\left[-2,\infty \right)$.

29. Domain is $\left(-\infty ,\infty \right)$ Range is $\left(-\infty ,11\right]$.

31. $f\left(x\right)={x}^{2}+1$

33. $f\left(x\right)=\frac{6}{49}{x}^{2}+\frac{60}{49}x+\frac{297}{49}$

35. $f\left(x\right)=-{x}^{2}+1$

37. Vertex $\left(1,\text{ }-1\right)$, Axis of symmetry is $x=1$. Intercepts are $\left(0,0\right), \left(2,0\right)$.

39. Vertex $\left(\frac{5}{2},\frac{-49}{4}\right)$, Axis of symmetry is $\left(0,-6\right),\left(-1,0\right),\left(6,0\right)$.

41. Vertex $\left(\frac{5}{4}, -\frac{39}{8}\right)$, Axis of symmetry is $x=\frac{5}{4}$. Intercepts are $\left(0, -8\right)$.

43. 50 feet

45. 50 feet by 50 feet. Maximize $f\left(x\right)=-{x}^{2}+100x$.

47. 125 feet by 62.5 feet. Maximize $f\left(x\right)=-2{x}^{2}+250x$.

49. 6 and –6; product is –36; maximize $f\left(x\right)={x}^{2}+12x$.

51. 2909.56 meters

53. $10.70