Chapter 3

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=5 x^{2}-3\) (a) Shifted left 10 units and downward 6 units (b) Shifted right 1 unit and upward 10 units

Simplify by using the imaginary unit \(i\). $$ \sqrt{-20} \cdot \sqrt{-5} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(x^{2}+2 x+1=0\) (b) \(x^{2}+2 x+1<0\) (c) \(x^{2}+2 x+1>0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ -3(x+5)^{2}-6=0 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=3 x^{2}-3 x+2\) (a) Shifted right 2000 units and upward 70 units (b) Shifted left 300 units and downward 30 units

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

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(12 z^{2}-23 z+10=0\) (b) \(12 z^{2}-23 z+10 \leq 0\) (c) \(12 z^{2}-23 z+10 \geq 0\)

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

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

Simplify by using the imaginary unit \(i\). $$ \sqrt{-15} \cdot \sqrt{-5} $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(18 z^{2}+9 z-20=0\) (b) \(18 z^{2}+9 z-20 \leq 0\) (c) \(18 z^{2}+9 z-20 \geq 0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ \frac{3}{4} x^{2}+\frac{1}{2} x-\frac{1}{2}=0 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=\sqrt{x}\) (a) Shifted right 4 units, reflected about the \(x\)-axis (b) Shifted left 2 units, reflected about the \(y\)-axis

Write the expression in standard form. $$ 3 i+5 i $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(x^{2}+2 x-1=0\) (b) \(x^{2}+2 x-1<0\) (c) \(x^{2}+2 x-1>0\)

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ -3 z^{2}-2 z+4=0 $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=\sqrt{x}\) (a) Reflected about the \(x\) -axis, shifted left 2 units (b) Reflected about the \(y\) -axis, shifted right 3 units

Write the expression in standard form. $$ -7 i+5 i $$

Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) \(x^{2}+4 x-3=0\) (b) \(x^{2}+4 x-3<0\) (c) \(x^{2}+4 x-3>0\)

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

Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. \(x^{2}+y^{2}=4 ;\) right 3 units, downward 4 units

Write the expression in standard form. $$ (3+i)+(-5-2 i) $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 25 k^{2}+1=10 k $$

Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. \(x^{2}+y^{2}=9 ;\) right 2 units, downward 6 units

Write the expression in standard form. $$ (-4+2 i)+(7+35 i) $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 49 k^{2}+4=-28 k $$

Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. \(x^{2}+y^{2}=5 ;\) left 5 units, upward 3 units

Write the expression in standard form. $$ 2 i-(-5+23 i) $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ -0.3 x^{2}+0.1 x=-0.02 $$

Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. \(x^{2}+y^{2}=7 ;\) left 3 units, downward 7 units

Write the expression in standard form. $$ (12-7 i)-(-1+9 i) $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ -0.1 x^{2}+1=0.5 x $$

Write the expression in standard form. $$ 3-(4-6 i) $$

Solve the inequality. $$ 2 x^{2}+5 x+2 \leq 0 $$

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

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

Write the expression in standard form. $$ (7+i)-(-8+5 i) $$

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ (2 x-1)(x+2)=(x+3)(x+1) $$

Write the expression in standard form. $$ (2)(2+4 i) $$

Solve the inequality. $$ x^{2}+x>6 $$

Solve the inequality. $$ -3 x \geq 9-12 x^{2} $$

Write the expression in standard form. $$ (-5)(-7+3 i) $$

Write the expression in standard form. $$ (1+i)(2-3 i) $$

Solve the inequality. $$ x^{2} \leq 4 $$

Solve the inequality. $$ 2 x^{2}>16 $$

Write the expression in standard form. $$ (-2+i)(1-2 i) $$

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

Solve the inequality. $$ x(x-4) \geq-4 $$

Solve the inequality. $$ x^{2}-3 x-10<0 $$

Write the expression in standard form. $$ (2-3 i)(1+4 i) $$