Chapter 9

$x=4\sqrt{3},x=\mathrm{-4}\sqrt{3}$

$y=3\sqrt{3},y=\mathrm{-3}\sqrt{3}$

$x=7,x=\mathrm{-7}$

$m=4,m=\mathrm{-4}$

$c=2\sqrt{3}i,\text{<mspace width="0.2em"> <mi>c</mi> <mo>=</mo> <mn>−2</mn> <msqrt> <mn>3</mn> </msqrt> <mi>i</mi> </mspace>}$

$c=2\sqrt{6}i,\text{<mspace width="0.2em"> <mi>c</mi> <mo>=</mo> <mn>−2</mn> <msqrt> <mn>6</mn> </msqrt> <mi>i</mi> </mspace>}$

$x=2\sqrt{10},x=\mathrm{-2}\sqrt{10}$

$y=2\sqrt{7},y=\mathrm{-2}\sqrt{7}$

$r=\frac{6\sqrt{5}}{5},r=-\frac{6\sqrt{5}}{5}$

$t=\frac{8\sqrt{3}}{3},t=-\frac{8\sqrt{3}}{3}$

$a=3+3\sqrt{2},a=3-3\sqrt{2}$

$b=\mathrm{-2}+2\sqrt{10},b=\mathrm{-2}-2\sqrt{10}$

$x=\frac{1}{2}+\frac{\sqrt{5}}{2}$,$x=\frac{1}{2}-\frac{\sqrt{5}}{2}$

$y=-\frac{3}{4}+\frac{\sqrt{7}}{4},y=-\frac{3}{4}-\frac{\sqrt{7}}{4}$

$a=5+2\sqrt{5},a=5-2\sqrt{5}$

$b=\mathrm{-3}+4\sqrt{2},b=\mathrm{-3}-4\sqrt{2}$

$r=-\frac{4}{3}+\frac{2\sqrt{2}i}{3},\text{r}=-\frac{4}{3}-\frac{2\sqrt{2}i}{3}$

$t=4+\frac{\sqrt{10}i}{2},\text{t}=4-\frac{\sqrt{10}i}{2}$

$m=\frac{7}{3},m=\mathrm{-1}$

$n=-\frac{3}{4},n=-\frac{7}{4}$

ⓐ ${\left(a-10\right)}^2$ ⓑ ${\left(b-\frac{5}{2}\right)}^2$
ⓒ ${\left(p+\frac{1}{8}\right)}^2$

ⓐ ${\left(b-2\right)}^2$ ⓑ ${\left(n+\frac{13}{2}\right)}^2$
ⓒ ${\left(q-\frac{1}{3}\right)}^2$

$x=\mathrm{-5},x=\mathrm{-1}$

$y=1,y=9$

$y=5+\sqrt{15}i,\text{<mspace width="0.2em"> <mi>y</mi> <mo>=</mo> <mn>5</mn> <mo>−</mo> <msqrt> <mrow> <mn>15</mn> </mrow> </msqrt> <mi>i</mi> </mspace>}$

$z=\mathrm{-4}+\sqrt{3}i,\text{z}=\mathrm{-4}-\sqrt{3}i$

$x=8+4\sqrt{3},\text{<mspace width="0.2em"> <mi>x</mi> <mo>=</mo> <mn>8</mn> <mo>−</mo> <mn>4</mn> <msqrt> <mn>3</mn> </msqrt> </mspace>}$

$y=\mathrm{-4}+3\sqrt{3},\text{y}=\mathrm{-4}-3\sqrt{3}$

$a=\mathrm{-7},a=3$

$b=\mathrm{-10},b=2$

$p=\frac{5}{2}+\frac{\sqrt{61}}{2},\text{<mspace width="0.2em"> <mi>p</mi> <mo>=</mo> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> <mo>−</mo> <mfrac> <mrow> <msqrt> <mrow> <mn>61</mn> </mrow> </msqrt> </mrow> <mn>2</mn> </mfrac> </mspace>}$

$q=\frac{7}{2}+\frac{\sqrt{37}}{2},\text{q}=\frac{7}{2}-\frac{\sqrt{37}}{2}$

$c=\mathrm{-9},c=3$

$d=11,d=\mathrm{-7}$

$m=\mathrm{-7},m=\mathrm{-1}$

$n=\mathrm{-2},n=8$

$r=-\frac{7}{3},r=3$

$t=-\frac{5}{2},t=2$

$x=-\frac{3}{8}+\frac{\sqrt{41}}{8},\text{<mspace width="0.2em"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>8</mn> </mfrac> <mo>−</mo> <mfrac> <mrow> <msqrt> <mrow> <mn>41</mn> </mrow> </msqrt> </mrow> <mn>8</mn> </mfrac> </mspace>}$

$y=\frac{5}{3}+\frac{\sqrt{10}}{3},\text{<mspace width="0.2em"> <mi>y</mi> <mo>=</mo> <mfrac> <mn>5</mn> <mn>3</mn> </mfrac> <mo>−</mo> <mfrac> <mrow> <msqrt> <mrow> <mn>10</mn> </mrow> </msqrt> </mrow> <mn>3</mn> </mfrac> </mspace>}$

$y=1,y=\frac{2}{3}$

$z=1,z=-\frac{3}{2}$

$a=\mathrm{-3},a=5$

$b=\mathrm{-6},b=\mathrm{-4}$

$m=\frac{\mathrm{-6}+\sqrt{15}}{3},m=\frac{\mathrm{-6}-\sqrt{15}}{3}$

$n=\frac{\mathrm{-2}+2\sqrt{6}}{5},n=\frac{\mathrm{-2}-2\sqrt{6}}{5}$

$a=\frac{1}{4}+\frac{\sqrt{31}}{4}i,\text{<mspace width="0.2em"> <mi>a</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>−</mo> <mfrac> <mrow> <msqrt> <mrow> <mn>31</mn> </mrow> </msqrt> </mrow> <mn>4</mn> </mfrac> <mi>i</mi> </mspace>}$

$b=-\frac{1}{5}+\frac{\sqrt{19}}{5}i,\text{<mspace width="0.2em"> <mi>b</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> <mo>−</mo> <mfrac> <mrow> <msqrt> <mrow> <mn>19</mn> </mrow> </msqrt> </mrow> <mn>5</mn> </mfrac> <mi>i</mi> </mspace>}$

$x=\mathrm{-1}+\sqrt{6},x=\mathrm{-1}-\sqrt{6}$

$y=1+\sqrt{2},y=1-\sqrt{2}$

$c=\frac{2+\sqrt{7}}{3},\text{<mspace width="0.2em"> <mi>c</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mo>−</mo> <msqrt> <mn>7</mn> </msqrt> </mrow> <mn>3</mn> </mfrac> </mspace>}$

$d=\frac{9+\sqrt{33}}{4},\text{d}=\frac{9-\sqrt{33}}{4}$

$r=\mathrm{-5}$

$t=\frac{4}{5}$

ⓐ 2 complex solutions; ⓑ 2 real solutions; ⓒ 1 real solution

ⓐ 2 real solutions; ⓑ 2 complex solutions; ⓒ 1 real solution

ⓐ factoring; ⓑ Square Root Property; ⓒ Quadratic Formula

ⓐ Quadratic Forumula;
ⓑ Factoring or Square Root Property ⓒ Square Root Property

$x=\sqrt{2},x=\text{−}\sqrt{2},x=2,x=\mathrm{-2}$

$x=\sqrt{7},x=\text{−}\sqrt{7},x=2,x=\mathrm{-2}$

$x=3,x=1$

$y=\mathrm{-1},y=1$

$x=9,x=16$

$x=4,x=16$

$x=\mathrm{-8},x=343$

$x=81,x=625$

$x=\frac{4}{3}x=2$

$x=\frac{2}{5},x=\frac{3}{4}$

The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11

The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.

The height of the triangle is 12 inches and the base is 76 inches.

The height of the triangle is 11 feet and the base is 20 feet.

The length of the garden is approximately 18 feet and the width 11 feet.

The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.

The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.

The distance between the opposite corners is approximately 7.2 feet.

The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.

The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.

The speed of the jet stream was 100 mph.

The speed of the jet stream was 50 mph.

Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.

The red hose take 6 hours and the green hose take 3 hours alone.

ⓐ up; ⓑ down

ⓐ down; ⓑ up

ⓐ $x=2;$ ⓑ $(2,\mathrm{-7})$

ⓐ $x=1;$ ⓑ $(1,\mathrm{-5})$

y-intercept: $(0,\mathrm{-8})$ x-intercepts $(\mathrm{-4},0),(2,0)$

y-intercept: $(0,\mathrm{-12})$ x-intercepts $(\mathrm{-2},0),(6,0)$

y-intercept: $(0,4)$ no x-intercept

y-intercept: $(0,\mathrm{-5})$ x-intercepts $(\mathrm{-1},0),(5,0)$

The minimum value of the quadratic function is −4 and it occurs when x = 4.

The maximum value of the quadratic function is 5 and it occurs when x = 2.

It will take 4 seconds for the stone to reach its maximum height of 288 feet.

It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.

ⓐ

ⓑ The graph of $g\left(x\right)=x^2+1$ is the same as the graph of $f\left(x\right)=x^2$ but shifted up 1 unit. The graph of $h\left(x\right)=x^2-1$ is the same as the graph of $f\left(x\right)=x^2$ but shifted down 1 unit.

ⓐ

ⓑ The graph of $h\left(x\right)=x^2+6$ is the same as the graph of $f\left(x\right)=x^2$ but shifted up 6 units. The graph of $h\left(x\right)=x^2-6$ is the same as the graph of $f\left(x\right)=x^2$ but shifted down 6 units.

ⓐ

ⓑ The graph of $g\left(x\right)={\left(x+2\right)}^2$ is the same as the graph of $f\left(x\right)=x^2$ but shifted left 2 units. The graph of $h\left(x\right)={(x-2)}^2$ is the same as the graph of $f\left(x\right)=x^2$ but shift right 2 units.

ⓐ

ⓑ The graph of $g\left(x\right)={\left(x+5\right)}^2$ is the same as the graph of $f\left(x\right)=x^2$ but shifted left 5 units. The graph of $h\left(x\right)={(x-5)}^2$ is the same as the graph of $f\left(x\right)=x^2$ but shifted right 5 units.

$f\left(x\right)=\mathrm{-4}{\left(x+1\right)}^2+5$

$f\left(x\right)=2{\left(x-2\right)}^2-5$

ⓐ $f(x)=3{(x-1)}^2+2$
ⓑ

ⓐ $f(x)=\mathrm{-2}{(x-2)}^2+1$
ⓑ

$f(x)={(x-3)}^2-4$

$f(x)={(x+3)}^2-1$

ⓐ

ⓑ $\left(\mathrm{-4},\mathrm{-2}\right)$

ⓐ

ⓑ $\left(\text{−}\infty ,2\right]\cup \left[6,\infty \right)$

ⓐ

ⓑ $\left(\mathrm{-1},5\right)$

ⓐ

ⓑ $\left(\text{−}\infty ,2\right]\cup \left[8,\infty \right)$

$\left(\text{−}\infty ,\mathrm{-4}\right]\cup \left[2,\infty \right)$

$\left[\mathrm{-3},5\right]$

$\left[\mathrm{-1}-\sqrt{2},\mathrm{-1}+\sqrt{2}\right]$

$\left(\text{−}\infty ,4-\sqrt{2}\right)\cup \left(4+\sqrt{2},\infty \right)$

ⓐ $\left(\text{−}\infty ,\infty \right)$
ⓑ no solution

ⓐ no solution
ⓑ $\left(\text{−}\infty ,\infty \right)$

$a=\pm 7$

$r=\pm 2\sqrt{6}$

$u=\pm 10\sqrt{3}$

$m=\pm 3$

$x=\pm 6$

$x=\pm 5i$

$x=\pm 3\sqrt{7}i$

$x=\pm 9$

$a=\pm 2\sqrt{5}$

$p=\pm \frac{4\sqrt{7}}{7}$

$y=\pm \frac{4\sqrt{10}}{5}$

$u=14,u=\mathrm{-2}$

$m=6\pm 2\sqrt{5}$

$r=\frac{1}{2}\pm \frac{\sqrt{3}}{2}$

$y=-\frac{2}{3}\pm \frac{2\sqrt{2}}{9}$

$a=7\pm 5\sqrt{2}$

$x=\mathrm{-3}\pm 2\sqrt{2}$

$c=-\frac{1}{5}\pm \frac{3\sqrt{3}}{5}i$

$x=\frac{3}{4}\pm \frac{\sqrt{7}}{2}i$

$m=2\pm 2\sqrt{2}$

$x=3+2\sqrt{3},x=3-2\sqrt{3}$

$x=-\frac{3}{5},x=\frac{9}{5}$

$x=-\frac{7}{6},x=\frac{11}{6}$

$r=\pm 4$

$a=4\pm 2\sqrt{7}$

$w=1,w=\frac{5}{3}$

$a=\pm 3\sqrt{2}$

$p=\frac{1}{3}\pm \frac{\sqrt{7}}{3}$

$m=\pm 2\sqrt{2i}$

$u=7\pm 6\sqrt{2}$

$m=4\pm 2\sqrt{3}$

$x=\mathrm{-3},x=\mathrm{-7}$

$c=\pm \frac{5\sqrt{6}}{6}$

$x=6\pm 2i$

Answers will vary.

ⓐ ${\left(m-12\right)}^2$ ⓑ ${\left(x-\frac{11}{2}\right)}^2$
ⓒ ${\left(p-\frac{1}{6}\right)}^2$

ⓐ ${\left(p-11\right)}^2$ ⓑ ${\left(y+\frac{5}{2}\right)}^2$
ⓒ ${\left(m+\frac{1}{5}\right)}^2$

$u=\mathrm{-3},u=1$

$x=\mathrm{-1},x=21$

$m=\mathrm{-2}\pm 2\sqrt{10}i$

$r=\mathrm{-3}\pm \sqrt{2}i$

$a=5\pm 2\sqrt{5}$

$x=-\frac{5}{2}\pm \frac{\sqrt{33}}{2}$

$u=1,u=13$

$r=\mathrm{-2},r=6$

$v=\frac{9}{2}\pm \frac{\sqrt{89}}{2}$

$x=5\pm \sqrt{30}$

$x=\mathrm{-7},x=3$

$x=\mathrm{-5},x=\mathrm{-1}$

$m=\mathrm{-11},m=1$

$n=1\pm \sqrt{14}$

$c=\mathrm{-2},c=\frac{3}{2}$

$x=\mathrm{-5},x=\frac{3}{2}$

$p=-\frac{7}{4}\pm \frac{\sqrt{161}}{4}$

$x=\frac{3}{10}\pm \frac{\sqrt{191}}{10}i$

Answers will vary.

$m=\mathrm{-1},m=\frac{3}{4}$

$p=\frac{1}{2},p=3$

$p=\mathrm{-4},p=\mathrm{-3}$

$r=\mathrm{-3},r=11$

$u=\frac{\mathrm{-7}\pm \sqrt{73}}{6}$

$a=\frac{3\pm \sqrt{3}}{2}$

$x=\mathrm{-4}\pm 2\sqrt{5}$

$y=\mathrm{-2},y=\frac{1}{3}$

$x=-\frac{3}{4}\pm \frac{\sqrt{15}}{4}i$

$x=\frac{3}{8}\pm \frac{\sqrt{7}}{8}i$

$v=2\pm 2\sqrt{13}$

$y=\mathrm{-4},y=7$

$m=\mathrm{-1},m=\frac{3}{4}$

$b=\frac{\mathrm{-2}\pm \sqrt{11}}{6}$

$c=-\frac{3}{4}$

$q=-\frac{3}{5}$

ⓐ $\text{no real solutions}$ ⓑ $1$
ⓒ $2$

ⓐ $1$ ⓑ $\text{no real solutions}$
ⓒ $2$

ⓐ $\text{factor}$ ⓑ $\text{square root}$
ⓒ $\text{Quadratic Formula}$

ⓐ $\text{Quadratic Formula}$
ⓑ $\text{square root}$ ⓒ $\text{factor}$

Answers will vary.

$x=\pm \sqrt{3},x=\pm 2$

$x=\pm \sqrt{15},x=\pm \sqrt{2}i$

$x=\pm 1,x=\frac{\pm \sqrt{6}}{2}$

$x=\pm \sqrt{3},x=\pm \frac{\sqrt{2}}{2}$

$x=\mathrm{-1},x=12$

$x=-\frac{5}{3},x=0$

$x=0,x=\pm \sqrt{3}$

$x=\pm \sqrt{\frac{11}{2}},x=\pm \sqrt{7}$

$x=25$

$x=4$

$x=\frac{1}{4}$

$x=\frac{1}{25},x=\frac{9}{4}$

$x=\mathrm{-1},x=\mathrm{-512}$

$x=8,x=\mathrm{-216}$

$x=\frac{27}{8},x=-\frac{64}{27}$

$x=\frac{27}{512},x=125$

$x=1,x=49$

$x=\mathrm{-2},x=-\frac{3}{5}$

$x=\mathrm{-2},x=\frac{4}{3}$