Chapter 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. \(3 x+6=-6 x^{2}\)

Solve each inequality using a graph, a table, or algebraically. $$ 4 x^{2}+20 x+25 \geq 0 $$

Graph each function. $$ y=-4 x^{2}+16 x-11 $$

Simplify. $$ (15+3 i)-(9-3 i) $$

Solve each equation by completing the square. \(x^{2}-4 x+5=0\)

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

Solve each equation by factoring. \(4 x^{2}-17 x=-4\)

PHYSICS For Exercises \(34-36,\) use the following information. An object is fired straight up from the top of a 200 -foot tower at a velocity of 80 feet per second. The height \(h(t)\) of the object \(t\) seconds after firing is given by \(h(t)=-16 t^{2}+80 t+200\) Interpret the meaning of the \(y\) -intercept in the context of this problem.

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. \(\frac{3}{4} x^{2}-\frac{1}{3} x-1=0\)

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}+12 x<-36 $$

Graph each function. $$ y=-5 x^{2}-40 x-80 $$

Simplify. $$ (3-4 i)-(1-4 i) $$

Solve each equation by completing the square. \(x^{2}+6 x+13=0\)

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

Solve each equation by factoring. \(4 x^{2}+8 x=-3\)

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. $$ f(x)=3 x^{2}+6 x-1 $$

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. \(.4 x^{2}+x-0.3=0\)

Solve each inequality using a graph, a table, or algebraically. $$ -x^{2}+14 x-49 \geq 0 $$

Graph each function. $$ y=-\frac{1}{2} x^{2}+5 x-\frac{27}{2} $$

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

Solve each equation by completing the square. \(x^{2}-10 x+28=0\)

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

Solve each equation by factoring. \(6 x^{2}+6=-13 x\)

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. $$ f(x)=-2 x^{2}+8 x-3 $$

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. \(0.2 x^{2}+0.1 x+0.7=0\)

Solve each inequality using a graph, a table, or algebraically. $$ 18 x-x^{2} \leq 81 $$

Graph each function. $$ y=\frac{1}{3} x^{2}-4 x+15 $$

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

Solve each equation by completing the square. \(x^{2}+8 x+9=-9\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 0.5 x^{2}-3=0 $$

Solve each equation by factoring. \(9 x^{2}+30 x=-16\)

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. $$ f(x)=-3 x^{2}-4 x $$

Solve each equation by using the method of your choice. Find exact solutions. \(-4(x+3)^{2}=28\)

Solve each inequality using a graph, a table, or algebraically. $$ 16 x^{2}+9<24 x $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=-3 x^{2}+12 x $$

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

NUMBER THEORY Use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist. Their sum is \(-17\) and their product is 72

Solve each equation by factoring. \(16 x^{2}-48 x=-27\)

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. $$ f(x)=2 x^{2}+5 x $$

Solve each equation by using the method of your choice. Find exact solutions. \(3 x^{2}-10 x=7\)

Solve each inequality using a graph, a table, or algebraically. $$ (x-1)(x+4)(x-3)>0 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=4 x^{2}+24 x $$

Simplify. $$ \frac{4}{5+3 i} $$

A picture has a square frame that is 2 inches wide. The area of the picture is one third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?

NUMBER THEORY Use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist. Their sum is 7 and their product is \(14 .\)

Find the roots of \(x(x+6)(x-5)=0\)

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. $$ f(x)=0.5 x^{2}-1 $$

Solve each equation by using the method of your choice. Find exact solutions. \(x^{2}+9=8 x\)

BUSINESS A mall owner has determined that the relationship between monthly rent charged for store space \(r\) (in dollars per square foot) and monthly profit \(P(r)\) (in thousands of dollars) can be approximated by the function \(P(r)=-8.1 r^{2}+46.9 r-38.2 .\) Solve each quadratic equation or inequality. Explain what each answer tells about the relationship between monthly rent and profit for this mall.

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=4 x^{2}+8 x-3 $$