Chapter 10

$x=9,x=\mathrm{-9}$

$y=11,y=\mathrm{-11}$

$x=5\sqrt{2},x=\mathrm{-5}\sqrt{2}$

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

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

$z=6,z=\mathrm{-6}$

no real solution

no real solution

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

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

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

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

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

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

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

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

$x=\frac{1}{3}+\frac{\sqrt{5}}{3},x=\frac{1}{3}-\frac{\sqrt{5}}{3}$

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

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

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

no real solution

no real solution

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

$y=\mathrm{-6}+4\sqrt{2},y=\mathrm{-6}-4\sqrt{2}$

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

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

${\left(y+6\right)}^2$

${\left(z+4\right)}^2$

${\left(a-10\right)}^2$

${\left(b-2\right)}^2$

${\left(m-\frac{5}{2}\right)}^2$

${\left(n+\frac{13}{2}\right)}^2$

${\left(p+\frac{1}{8}\right)}^2$

${\left(q-\frac{1}{3}\right)}^2$

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

$d=\mathrm{-9},d=\mathrm{-1}$

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

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

no real solution

no real solution

$x=8\pm 4\sqrt{3}$

$y=\mathrm{-4}\pm 3\sqrt{3}$

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

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

$p=\frac{5}{2}\pm \frac{\sqrt{61}}{2}$

$q=\frac{7}{2}\pm \frac{\sqrt{37}}{2}$

$c=\mathrm{-3}\pm 4\sqrt{2}$

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

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

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

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

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

$x=-\frac{3}{8}\pm \frac{\sqrt{201}}{8}$

$y=-\frac{3}{10}\pm \frac{\sqrt{209}}{10}$

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

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

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

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

$p=\frac{\mathrm{-4}\pm \sqrt{6}}{2}$

$q=\frac{11\pm \sqrt{61}}{10}$

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

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

no real solution

no real solution

$x=\mathrm{-1}\pm \sqrt{6}$

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

$c=\frac{2\pm \sqrt{7}}{3}$

$d=\frac{2}{3},d=0$

$r=\mathrm{-5}$

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

ⓐ no real solutions ⓑ 2 ⓒ 1 ⓓ no real solutions

ⓐ 2 ⓑ no real solutions ⓒ 1 ⓓ 2

ⓐ factor ⓑ Square Root Property ⓒ Quadratic Formula

ⓐ Quadratic Formula ⓑ factoring ⓒ Square Root Property

Two consecutive odd numbers whose product is 99 are 9 and 11, and $\mathrm{-9}$ and $\mathrm{-11}$.

Two consecutive even numbers whose product is 168 are 12 and 14,and $\mathrm{-12}$ and $\mathrm{-14}$.

The height of the triangle is 8 inches and the width is 52 inches.

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

The length of the shadow is 6.3 feet and the length of the flag pole is 18.9 ft.

The distance to the opposite corner is 3.2.

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

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

The arrow will reach 180 on its way up in 3 seconds, and on the way down in 3.8 seconds.

The ball will reach 48 feet on its way up in .6 seconds and on the way down in 5.5 seconds.

ⓐ up ⓑ down

ⓐ down ⓑ up

ⓐ $x=2$ ⓑ $\left(2,\mathrm{-7}\right)$

ⓐ $x=1$ ⓑ $\left(1,\mathrm{-5}\right)$

$y\text{:}\left(0,\mathrm{-8}\right);x\text{:}\left(\mathrm{-4},0\right),\left(2,0\right)$

$y\text{:}\left(0,\mathrm{-12}\right);x\text{:}\left(6,0\right),\left(\mathrm{-2},0\right)$

$y\text{:}\left(0,4\right);x\text{:}\text{none}$

$y\text{:}\left(0,\mathrm{-5}\right);x\text{:}(5,0)(\mathrm{-1},0)$

$y\text{:}\left(0,\mathrm{-36}\right);x\text{:}\left(\mathrm{-6},0\right)$

$y\text{:}\left(0,4\right);x\text{:}\left(-\frac{2}{3},0\right)$

$y\text{:}\left(0,\mathrm{-8}\right)$; $x\text{:}\left(2,0\right),\left(\mathrm{-4},0\right)$;
axis: $x=\mathrm{-1}$; vertex: $\left(\mathrm{-1},\mathrm{-9}\right)$;

$y\text{:}\left(0,12\right);x\text{:}\left(2,0\right),\left(6,0\right);$
axis: $x=4;\text{vertex:}\left(4,\mathrm{-4}\right)$;

$y\text{:}\left(0,\mathrm{-12}\right);x\text{:}\left(2,0\right);$
axis: $x=2;\text{vertex:}\left(2,0\right)$;

$y\text{:}\left(0,1\right);x\text{:}\left(-\frac{1}{5},0\right);$
axis: $x=-\frac{1}{5};\text{vertex:}\left(-\frac{1}{5},0\right)$;

$y\text{:}\left(0,5\right);x\text{:}\text{none};$
axis: $x=\frac{3}{2};\text{vertex:}\left(\frac{3}{2},\frac{1}{2}\right)$;

$y\text{:}\left(0,\mathrm{-1}\right);x\text{:}\text{none};$
axis: $x=0;\text{vertex:}\left(0,\mathrm{-1}\right)$;

$y\text{:}\left(0,3\right);x\text{:}\left(\mathrm{-1.6},0\right),\left(\mathrm{-0.4},0\right);$
axis: $x=\mathrm{-1};\text{vertex:}\left(\mathrm{-1},\mathrm{-2}\right)$;

$y\text{:}\left(0,5\right);x\text{:}\left(0.6,0\right),\left(\mathrm{-2.6},0\right);$
axis: $x=\mathrm{-1};\text{vertex:}\left(\mathrm{-1},8\right)$;

The minimum value is $\mathrm{-4}$ when $x=4$.

The maximum value is 5 when $x=2$.

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

It will take 6.5 seconds to reach the maximum height of 676 feet.

$a=\pm 7$

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

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

$m=\pm 3$

no real solution

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

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

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

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

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

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

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

no real solution

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

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

$r=\pm 4$

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

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

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

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

no real solution

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

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

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

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

no real solution

4 feet

Answers will vary.

${\left(a+5\right)}^2$

${\left(m+9\right)}^2$

${\left(m-12\right)}^2$

${\left(p-11\right)}^2$

${\left(x-\frac{9}{2}\right)}^2$

${\left(p-\frac{1}{6}\right)}^2$

$v=\mathrm{-10},v=4$

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

$c=\mathrm{-1},c=13$

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

no real solution

no real solution

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

$u=1,u=13$

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

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

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

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

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

16 feet, 20 feet

ⓐ $\mathrm{-5}$ ⓑ $\mathrm{-5}$ ⓒ Answers will vary.

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

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

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

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

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

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

no real solution

$v=\frac{\mathrm{-5}\pm \sqrt{65}}{2}$

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

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

$m=-\frac{7}{5},m=1$

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

$r=\frac{\mathrm{-3}\pm \sqrt{89}}{8}$

$a=\frac{\mathrm{-6}\pm \sqrt{26}}{2}$

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

$x=\frac{\mathrm{-6}\pm \sqrt{42}}{4}$

ⓐ no real solutions ⓑ 1
ⓒ 2 ⓓ no real solutions

ⓐ 1 ⓑ no real solutions
ⓒ 1 ⓓ 2

ⓐ factor ⓑ square root
ⓒ Quadratic Formula

ⓐ factor ⓑ square root
ⓒ factor

5 seconds, 8 seconds

ⓐ $\mathrm{-20},10$ ⓑ $\mathrm{-20},10$
ⓒ answers will vary

Two consecutive odd numbers whose product is 255 are 15 and 17, and $\mathrm{-15}$ and $\mathrm{-17}$.

Two consecutive even numbers whose product is 624 are 24 and 26, and $\mathrm{-26}$ and $\mathrm{-24}$.

Two consecutive odd numbers whose product is 483 are 21 and 23, and $\mathrm{-21}$ and $\mathrm{-23}$.

The width of the triangle is 5 inches and the height is 18 inches.

The leg of the right triangle is 1.7 feet and the hypotenuse is 3.4 feet.

The length of the fence is 7.1 units.

The width of the driveway is 10 feet and its length is 35 feet.

The rocket will reach 1,200 feet on its way up in 2 seconds and on the way down in 38 seconds.

70 seconds

ⓐ answers will vary
ⓑ answers will vary ⓒ answers will vary ⓓ answers will vary

down

up

ⓐ $x=\mathrm{-4}$ ⓑ $\left(\mathrm{-4},\mathrm{-17}\right)$

ⓐ $x=1$ ⓑ $\left(1,6\right)$

$y\text{:}(0,6);x\text{:}(\mathrm{-1},0),(\mathrm{-6},0)$

$y\text{:}(0,19);x\text{:}\text{none}$

$y\text{:}(0,25);x\text{:}(\frac{5}{2},0)$

$y\text{:}(0,5);x\text{:}(\mathrm{-1},0),(\mathrm{-5},0);$
axis: $x=\mathrm{-3};\text{vertex}\text{:}(\mathrm{-3},\mathrm{-4})$

$y\text{:}(0,3);x\text{:}(\mathrm{-1},0),(\mathrm{-3},0);$
axis: $x=\mathrm{-2};\text{vertex:}(\mathrm{-2},\mathrm{-1})$

$y\text{:}(0,4)x\text{:}(-\frac{2}{3},0);$
axis: $x=-\frac{2}{3};\text{vertex:}(-\frac{2}{3},0)$

$y\text{:}(0,\mathrm{-7});x\text{:}\text{none};$
axis: $x=1;\text{vertex}\text{:}(1,\mathrm{-6})$

$y\text{:}(0,1);x\text{:}(1.7,0),(0.3,0);$
axis: $x=1;\text{vertex}\text{:}(1,\mathrm{-1})$

$y\text{:}(0,2)x\text{:}(1,0);$
axis: $x=1;\text{vertex:}(1,0)$

$y\text{:}(0,2)x\text{:}(\mathrm{-4.4},0),(0.4,0);$
axis: $x=\mathrm{-2};\text{vertex:}(\mathrm{-2},6)$

$y\text{:}(0,8);x\text{:}\text{none};$
axis: $x=1;\text{vertex}\text{:}(1,3)$

$y\text{:}(0,20)x\text{:}(\mathrm{-4.5},0),(\mathrm{-1.5},0);$
axis: $x=\mathrm{-3};\text{vertex:}(\mathrm{-3},\mathrm{-7})$

The minimum value is $-\frac{9}{8}$ when $x=-\frac{1}{4}$.

The minimum value is 6 when $x=3$.

The maximum value is 16 when $x=0$.

In 5.3 sec the arrow will reach maximum height of 486 ft.

20 computers will give the maximum of $400 in receipts.

The length of the side along the river of the corral is 120 feet and the maximum area is 7,200 sq ft.

Answers will vary.

$x=\pm 10$

$m=\pm 2\sqrt{10}$

$a=\pm 5$

no solution

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

$c=\pm \frac{4\sqrt{5}}{5}$

$p=1,9$

$u=\mathrm{-1}\pm 3\sqrt{5}$

$x=\frac{1}{4}\pm \frac{\sqrt{3}}{4}$

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

no solution

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

$a=-\frac{3}{2},\frac{3}{4}$

${(x+11)}^2$

${\left(m-4\right)}^2$

${\left(a-\frac{3}{2}\right)}^2$

${\left(p+\frac{2}{5}\right)}^2$

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

$x=\mathrm{-4},8$

no solution

$v=7\pm 3\sqrt{2}$

$m=\mathrm{-9},\mathrm{-1}$

$a=\frac{3}{2}\pm \frac{\sqrt{41}}{2}$

$u=\mathrm{-6}\pm 2\sqrt{2}$

$p=0,6$

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

$c=-\frac{1}{3}\pm \frac{2\sqrt{7}}{3}$

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

$r=\mathrm{-6},7$

$v=-\frac{5}{4},1$

$m=\frac{\mathrm{-4}\pm \sqrt{10}}{3}$

no real solution

$u=5\pm \sqrt{22}$

$p=\frac{4\pm \sqrt{6}}{5}$

$c=-\frac{1}{2}$

ⓐ 1 ⓑ 2 ⓒ 2 ⓓ none

ⓐ factor ⓑ Quadratic Formula ⓒ square root

Two consecutive odd numbers whose product is 323 are 17 and 19, and $\mathrm{-17}$ and $\mathrm{-19}.$

The height of the banner is 13 cm and the length of the side is 54 cm.

The lengths of the sides of the mosaic are 2.2 and 4.4 feet.

The width of the front walk is 8.1 feet and its length is 30.8 feet.

The ball will reach 384 feet on its way up in 4 seconds and on the way down in 6 seconds.

down

up

ⓐ $x=3$ ⓑ $\left(3,17\right)$

$y\text{:}(0,5);x\text{:}(5,0),(\mathrm{-1},0)$

$y\text{:}\left(0,10\right);x\text{:}\text{none}$

$y\text{:}(0,1);x\text{:}\left(\frac{1}{4},0\right)$

$y\text{:}(0,15);x\text{:}(\mathrm{-3},0),(\mathrm{-5},0);$
axis: $x=\mathrm{-4};\text{vertex}\text{:}(\mathrm{-4},\mathrm{-1})$

$y\text{:}(0,\mathrm{-16});x\text{:}(4,0);$
axis: $x=4;\text{vertex}\text{:}(4,0)$

$y\text{:}(0,13);x\text{:}\text{none};$
axis: $x=\mathrm{-3};\text{vertex}\text{:}(\mathrm{-3},4)$