Chapter 12

Factor the expression. $$ x^{2}+12 x+36 $$

Solve the quadratic equation. $$ x^{2}+10 x-3=0 $$

Complete the statement with always, sometimes, or never. If \(a\) and \(b\) are whole numbers, then \(\sqrt{a^{2}+b^{2}}\) is _____ equal to \(a+b\)

Simplify the radical expression. $$ \frac{\sqrt{10}}{\sqrt{3}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=-\sqrt{2 x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{5 x+10}=-5 $$

MULTIPLE CHOICE Given the lengths of the three sides of a triangle, determine which triangle is not a right triangle. $$ A)a=9, b=40, c=41 $$ $$ B)a=3, b=4, c=5 $$ $$ C)a=7, b=24, c=25 $$ $$ D)a=10, b=49, c=50 $$

Factor the expression. $$ c^{2}-22 c+121 $$

Solve the quadratic equation. $$ x^{2}+16 x+9=0 $$

The shot (a metal sphere) used in the women's shot put has a volume of about 524 cubic centimeters. Find the radius of the shot.

Simplify the radical expression. $$ \frac{\sqrt{3}}{\sqrt{7}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=\sqrt{x}+4$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}+11=1 $$

Complete the statement using \(<,>,\) or \(=\). \(\frac{3}{1000} ? 0.03\)

Plot and label the ordered pairs in a coordinate plane. $$ A(2,5), B(0,-1), C(3,1) $$

Factor the expression. $$ 9 s^{2}+6 s+1 $$

Solve the quadratic equation. $$ x^{2}+22 x+1=0 $$

Evaluate the expression \(100^{3 / 2}\) (A) 10 (B) 100 (C) 1000 (D) \(10,000\)

Simplify the radical expression. $$ \frac{6}{6+\sqrt{3}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=\sqrt{x}-3$$

Solve the equation. Check for extraneous solutions. $$ x=\sqrt{x+42} $$

Complete the statement using \(<,>,\) or \(=\). \(0.23 ? \frac{23}{100}\)

Plot and label the ordered pairs in a coordinate plane. $$ A(2,-5), B(2,4), C(-3,0) $$

Factor the expression. $$ 4 n^{2}-64 $$

Solve the quadratic equation. $$ x^{2}+2 x-11=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 16+x^{2}=64 $$

Simplify the radical expression. $$ \frac{9}{5-\sqrt{7}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=5-\sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}-5=20 $$

Plot and label the ordered pairs in a coordinate plane. $$ A(-1,-2), B(-4,5), C(0,2) $$

Factor the expression. $$ 72-50 p^{2} $$

Solve the quadratic equation. $$ x^{2}+8 x-6=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}+25=81 $$

Simplify the radical expression. $$ \frac{1}{2+\sqrt{2}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=6-\sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x-10}=-1 $$

Plot and label the ordered pairs in a coordinate plane. $$ A(1,4), B(-2,-1), C(3,-1) $$

Factor the expression. $$ 60 y^{2}-240 $$

Solve the quadratic equation. $$ x^{2}+14 x-7=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}+81=144 $$

Simplify the radical expression. $$ \frac{6}{10+\sqrt{2}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=2 \sqrt{x}+3$$

Solve the equation. Check for extraneous solutions. $$ 3 \sqrt{x}=-21 $$

NUMBER OF X-INTERCEPTS Determine whether the graph of the function intersects the \(x\) -axis in zero, one, or two points. $$ y=x^{2}+2 x+15 $$

Factor the expression completely. $$ 3 y^{3}+15 y^{2}-18 y $$

Solve the quadratic equation. $$ x^{2}+20 x+2=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 4 x^{2}-144=0 $$

Simplify the radical expression. $$ \frac{\sqrt{5}}{3-\sqrt{5}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=5 \sqrt{x}-2$$

Solve the equation. Check for extraneous solutions. $$ x=\sqrt{2 x+3} $$