Chapter 3

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=(x-3)^{2}+1\)

Write the expression in standard form. $$ (-2+3 i)^{2} $$

Solve the inequality. $$ -x^{2}+x+6 \leq 0 $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ x^{2}+2 x=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=(x+2)^{2}-3\)

Solve the inequality. $$ -x^{2}-2 x+8>0 $$

Write the expression in standard form. $$ (2-3 i)^{2} $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ x^{2}-4=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=\frac{1}{4}(x+1)^{2}\)

Write the expression in standard form. $$ 2 i(1-i)^{2} $$

Solve the inequality. $$ 6 x^{2}-x<1 $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ x^{2}-x-6=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=2(x-4)^{2}\)

Solve the inequality. $$ 5 x^{2} \leq 10-5 x $$

Write the expression in standard form. $$ -i(5-2 i)^{2} $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ 2 x^{2}+5 x-3=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=-\sqrt{x+5}\)

Write the expression in standard form. $$ \frac{1}{1+i} $$

Solve the inequality. $$ (x+4)(x-10) \leq 0 $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ 2 x^{2}=6 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=-\sqrt{x}-3\)

Solve the inequality. $$ (x-3.1)(x+2.7)>0 $$

Write the expression in standard form. $$ \frac{1-i}{2+3 i} $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ x^{2}-225=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=2 \sqrt{-x}\)

Write the expression in standard form. $$ \frac{4+i}{5-i} $$

Solve the inequality. $$ 2 x^{2}+4 x+3<0 $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ 4 x(x-3)=-9 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=\sqrt{-\frac{1}{2} x}\)

Write the expression in standard form. $$ \frac{10}{1-4 i} $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ -4 x(x-1)=1 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=|-(x+1)|\)

Write the expression in standard form. $$ \frac{2 i}{10-5 i} $$

Solve the inequality. $$ 9 x^{2}+4>12 x $$

Solve the quadratic equation graphically. $$ 20 x^{2}+11 x=3 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=|4-x |\)

Solve the inequality. $$ x^{2}+2 x \geq 35 $$

Write the expression in standard form. $$ \frac{3-2 i}{1+2 i} $$

Solve the quadratic equation graphically. $$ -2 x^{2}+4 x=1.595 $$

Use transformations to sketch a graph of \(f\). \(f(x)=x^{2}-3\)

Write the expression in standard form. $$ \frac{3}{-i} $$

Solve the inequality. $$ x^{2} \geq x $$

Solve the quadratic equation graphically. $$ 2.5 x^{2}=4.75 x-2.1 $$

Use transformations to sketch a graph of \(f\). \(f(x)=-x^{2}\)

Solve the inequality. $$ x^{2} \geq-3 $$

Write the expression in standard form. $$ \frac{4-2 i}{i} $$

Solve the quadratic equation graphically. $$ x(x+24)=6912 $$

Use transformations to sketch a graph of \(f\). \(f(x)=(x-5)^{2}+3\)

Write the expression in standard form. $$ \frac{-2+i}{(1+i)^{2}} $$

Solve the equation by completing the square. $$ x^{2}+4 x-6=0 $$