Chapter 5

Graph each function. $$ y=\frac{1}{4}(x-2)^{2}+4 $$

ELECTRICITY The current in one part of a series circuit is \(4-j\) amps. The current in another part of the circuit is \(6+4 j\) amps. Add these complex numbers to find the total current in the circuit.

Solve each equation by completing the square. \(x^{2}-6 x+12=0\)

Write a quadratic equation in standard form with the given roots. \(4,-5\)

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=x^{2}-9 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(-3 x^{2}-5 x+2=0\)

Graph each inequality. $$ y>x^{2}+6 x+5 $$

Graph each function. $$ y=\frac{1}{2}(x-3)^{2}-5 $$

Simplify. $$ (-2+7 i)+(-4-5 i) $$

Solve each equation by using the Square Root Property. \(x^{2}+4 x+4=25\)

Write a quadratic equation in standard form with the given roots. \(-6,-8\)

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=2 x^{2}-4 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(9 x^{2}-6 x-4=-5\)

Graph each function. $$ y=x^{2}+6 x+2 $$

Simplify. $$ (8+6 i)-(2+3 i) $$

Solve each equation by using the Square Root Property. \(x^{2}-10 x+25=49\)

Factor each polynomial. \(x^{2}-7 x+6\)

Use the related graph of each equation to determine its solutions. $$ -0.5 x^{2}=0 $$

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=3 x^{2}+1 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(25+4 x^{2}=-20 x\)

Use the graph of the related function of each inequality to write its solutions. $$ x^{2}-4 x-12 \leq 0 $$

Graph each function. $$ y=x^{2}-8 x+18 $$

Simplify. $$ (3-5 i)(4+6 i) $$

Solve each equation by using the Square Root Property. \(x^{2}-9 x+\frac{81}{4}=\frac{1}{4}\)

Factor each polynomial. \(x^{2}+8 x-9\)

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=x^{2}-4 x+4 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}+3 x-3=0\)

Use the graph of the related function of each inequality to write its solutions. $$ x^{2}-9>0 $$

What is the effect on the graph of the equation \(y=x^{2}+2\) when the equation is changed to \(y=x^{2}-5 ?\)

Simplify. $$ (1+2 i)(-1+4 i) $$

Solve each equation by using the Square Root Property. \(x^{2}+7 x+\frac{49}{4}=4\)

Factor each polynomial. \(3 x^{2}+12 x-63\)

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=x^{2}-9 x+9 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}-16 x+4=0\)

What is the effect on the graph of the equation \(y=x^{2}+2\) when the equation is changed to \(y=3 x^{2}-5 ?\)

Simplify. $$ \frac{2-i}{5+2 i} $$

Solve each equation by using the Square Root Property. \(x^{2}+8 x+16=7\)

Factor each polynomial. \(5 x^{2}-80\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ x^{2}-3 x=0 $$

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=x^{2}-4 x-5 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(x^{2}+4 x+3=4\)

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}-3 x-18>0 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=-2(x+3)^{2} $$

Simplify. $$ \frac{3+i}{1+4 i} $$

Solve each equation by using the Square Root Property. \(x^{2}-6 x+9=8\)

Solve each equation by factoring. Then graph. \(x^{2}+5 x-24=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -x^{2}+4 x=0 $$

Complete parts a-c for each quadratic function. a. Find the \(y\) -intercept, the equation of the axis of symmetry, and the \(x\) -coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. $$ f(x)=x^{2}+12 x+36 $$

Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. \(2 x-5=-x^{2}\)

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}+3 x-28<0 $$