Chapter 8

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$x^{2}-7.4 x+13.69=0$$

Solve each inequality. State the solution set using interval notation when possible. \(z^{2} \geq 4(z+3)\)

Find all real and imaginary solutions to each equation. $$a^{4}+6 a^{2}+8=0$$

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$1.44 x^{2}+5.52 x+5.29=0$$

Solve each inequality. State the solution set using interval notation when possible. \(t^{2}<3(2 t-3)\)

a) Write the function \(y=3(x-2)^{2}+6\) in the form \(y=a x^{2}+b x+c,\) and find the vertex of the parabola using the formula \(x=\frac{-b}{2 a}\) b) Repeat part (a) with the functions \(y=-4(x-5)^{2}-9\) and \(y=3(x+2)^{2}-6\) c) What is the vertex for a parabola that is written in the form \(y=a(x-h)^{2}+k ?\) Explain your answer.

Find all real and imaginary solutions to each equation. $$b^{4}+13 b^{2}+36=0$$

Graph \(y=x^{2}, y=\frac{1}{2} x^{2},\) and \(y=2 x^{2}\) on the same coordinate system. What can you say about the graph of \(y=a x^{2} ?\)

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$1.85 x^{2}+6.72 x+3.6=0$$

Find all real and imaginary solutions to each equation. $$m^{4}-16=0$$

Graph \(y=x^{2}, y=(x-3)^{2},\) and \(y=(x+3)^{2}\) on the same coordinate system. How does the graph of \(y=(x-h)^{2}\) compare to the graph of \(y=x^{2} ?\)

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$3.67 x^{2}+4.35 x-2.13=0$$

Find all real and imaginary solutions to each equation. $$l^{4}-4=0$$

The equation \(x=y^{2}\) is equivalent to \(y=\pm \sqrt{x} .\) Graph both \(y=\sqrt{x}\) and \(y=-\sqrt{x}\) on a graphing calculator. How does the graph of \(x=y^{2}\) compare to the graph of \(y=x^{2} ?\)

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$3 x^{2}+14,379 x+243=0$$

Solve each inequality. State the solution set using interval notation when possible. \(\frac{1}{2} x^{2} \geq 4-x\)

Find all real and imaginary solutions to each equation. $$16 b^{4}-1=0$$

Graph each of the following equations by solving for \(y\) a) \(x=y^{2}-1\) b) \(x=-y^{2}\) c) \(x^{2}+y^{2}=4\)

Find all real and imaginary solutions to each equation. $$b^{4}-81=0$$

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$x^{2}+0.00075 x-0.0062=0$$

Find all real and imaginary solutions to each equation. $$x^{3}+1=0$$

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$4.3 x^{2}-9.86 x-3.75=0$$

Find all real and imaginary solutions to each equation. $$x^{3}-1=0$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. Missing numbers. Find two positive real numbers that differ by 1 and have a product of 16.

Solve each inequality. State the solution set using interval notation when possible. \((x-2)(x+1)(x-5) \geq 0\)

Find all real and imaginary solutions to each equation. $$x^{3}+8=0$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. Missing numbers. Find two positive real numbers that differ by 2 and have a product of \(10 .\)

Solve each inequality. State the solution set using interval notation when possible. \((x-1)(x+2)(2 x-5)<0\)

Find all real and imaginary solutions to each equation. $$x^{3}-27=0$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. More missing numbers. Find two real numbers that have a sum of 6 and a product of 4

Find all real or imaginary solutions to each equation. Use the method of your choice. $$x^{2}=-121$$

Find all real and imaginary solutions to each equation. $$a^{-2}-2 a^{-1}+5=0$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. More missing numbers. Find two real numbers that have a sum of 8 and a product of 2

Solve each inequality. State the solution set using interval notation when possible. \(x^{3}+5 x^{2}-4 x-20 \geq 0\)

Find all real or imaginary solutions to each equation. Use the method of your choice. $$w^{2}=-225$$

Find all real and imaginary solutions to each equation. $$b^{-2}-4 b^{-1}+6=0$$

Solve each inequality. State the solution set using interval notation when possible. \(0.23 x^{2}+6.5 x+4.3<0\)

Find all real or imaginary solutions to each equation. Use the method of your choice. $$4 x^{2}+25=0$$

Find all real and imaginary solutions to each equation. $$(2 x-1)^{2}-2(2 x-1)+5=0$$

Solve each inequality. State the solution set using interval notation when possible. \(0.65 x^{2}+3.2 x+5.1>0\)

Find all real or imaginary solutions to each equation. Use the method of your choice. $$5 w^{2}-3=0$$

Find all real and imaginary solutions to each equation. $$(4 x-1)^{2}-6(4 x-1)+25=0$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. Area of a rectangle. The length of a rectangle is \(4 \mathrm{ft}\) longer than the width, and its area is 10 square feet ( \(\mathrm{ft}^{2}\) ). Find the length and width.

Find all real or imaginary solutions to each equation. Use the method of your choice. $$\left(p+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. Diagonal of a square. The diagonal of a square is \(2 \mathrm{m}\) longer than a side. Find the length of a side.

Solve each inequality. State the solution set using interval notation when possible. \(\frac{x}{3-x}>\frac{2}{x+5}\)

Find all real or imaginary solutions to each equation. Use the method of your choice. $$\left(y-\frac{2}{3}\right)^{2}=\frac{4}{9}$$

Find the exact solution \((s)\) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. Projected pine cone. If a pine cone is projected upward at a velocity of \(16 \mathrm{ft} / \mathrm{sec}\) from the top of a 96 -foot pine tree, then how long does it take to reach the earth?

Find all real or imaginary solutions to each equation. Use the method of your choice. $$5 t^{2}+4 t-3=0$$

Find all real or imaginary solutions to each equation. Use the method of your choice. $$3 v^{2}+4 v-1=0$$