Chapter 3

Simplify by using the imaginary unit \(i\). $$ \sqrt{-4} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ x^{2}+x-11=1 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-16} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ x^{2}-9 x+10=-8 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-100} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ t^{2}=2 t $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-49} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ t^{2}-7 t=0 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-23} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 3 x^{2}-7 x=0 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-11} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 5 x=9 x^{2} $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-12} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 2 z^{2}=13 z+15 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-32} $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 4 z^{2}=7-27 z $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-54} $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=x^{2} ;\) right 2 units, downward 3 units

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ x(3 x+14)=5 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-28} $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=3 x-4 ;\) left 3 units, upward 1 unit

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ x(5 x+19)=4 $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=x^{2}-4 x+1 ;\) left 6 units, upward 4 units

Simplify by using the imaginary unit \(i\). $$ \frac{4 \pm \sqrt{-16}}{2} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(x^{2}-x-12=0\) (b) \(x^{2}-x-12<0\) (c) \(x^{2}-x-12>0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 6 x^{2}+\frac{5}{2}=8 x $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=x^{2}-x-2 ;\) right 2 units, upward 3 units

Simplify by using the imaginary unit \(i\). $$ \frac{-2 \pm \sqrt{-36}}{6} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(x^{2}-8 x+12=0\) (b) \(x^{2}-8 x+12<0\) (c) \(x^{2}-8 x+12>0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 8 x^{2}+63=-46 x $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=\frac{1}{2} x^{2}+2 x-1 ;\) left 3 units, downward 2 units

Simplify by using the imaginary unit \(i\). $$ \frac{-6 \pm \sqrt{-72}}{3} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(\mathrm{k}^{2}-5=0\) (b) \(\mathrm{k}^{2}-5 \leq 0\) (c) \(\mathrm{k}^{2}-5 \geq 0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ (t+3)^{2}=5 $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=5-3 x-\frac{1}{2} x^{2} ;\) right 5 units, downward 8 units

Simplify by using the imaginary unit \(i\). $$ \frac{2 \pm \sqrt{-8}}{4} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(\mathrm{n}^{2}-17=0\) (b) \(\mathrm{n}^{2}-17 \leq 0\) (c) \(\mathrm{n}^{2}-17 \geq 0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ (t-2)^{2}=11 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=3 x^{2}+2 x-5\) (a) Shifted left 3 units (b) Shifted downward 4 units

Simplify by using the imaginary unit \(i\). $$ \sqrt{-5} \cdot \sqrt{-5} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(3 x^{2}+8 x=0\) (b) \(3 x^{2}+8 x \leq 0\) (c) \(3 x^{2}+8 x \geq 0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 4 x^{2}-13=0 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=2 x^{2}-3 x+2\) (a) Shifted right 8 units (b) Shifted upward 2 units

Simplify by using the imaginary unit \(i\). $$ \sqrt{-8} \cdot \sqrt{-8} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(7 \mathrm{x}^{2}-4 \mathrm{x}=0\) (b) \(7 \mathrm{x}^{2}-4 \mathrm{x} \leq 0\) (c) \(7 \mathrm{x}^{2}-4 \mathrm{x} \geq 0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 9 x^{2}-11=0 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=2 x^{2}-4 x+1\) (a) Shifted right 2 units and upward 4 units. (b) Shifted left 8 units and downward 5 units.

Simplify by using the imaginary unit \(i\). $$ \sqrt{-18} \cdot \sqrt{-2} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(-4 x^{2}+12 x-9=0\) (b) \(-4 x^{2}+12 x-9<0\) (c) \(-4 x^{2}+12 x-9>0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 2(x-1)^{2}+4=0 $$