Chapter 3

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=2 x^{3}-3 x^{2}-11 x+6 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-2(x+1)^{2}+5 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 9 x^{2}+3 x-2 \geq 0 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and the square of z.

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=2 x^{3}-5 x^{2}+x+2 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-2(x+4)^{2}-8 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 2 x^{2}+x<15 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube of z and inversely as y.

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=x^{3}+4 x^{2}-3 x-6 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=2 x^{2}-8 x+3 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 6 x^{2}+x>1 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube root of z and inversely as y.

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=2 x^{3}+x^{2}-3 x+1 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=3 x^{2}-12 x+1 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 4 x^{2}+7 x<-3 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square root of w.

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=2 x^{3}+6 x^{2}+5 x+2 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-x^{2}-2 x+8 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}+16 x<-5 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square of w.

In Exercises \(9-16\) a. List all possible rational zeros. b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=x^{3}-4 x^{2}+8 x-5 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-2 x^{2}+8 x-1 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the sum of y and w.

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 5 x \leq 2-3 x^{2} $$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{3}-2 x^{2}-11 x+12=0 $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$ f(x)=(x-4)^{2}-1 $$

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the difference between y and w.

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 4 x^{2}+1 \geq 4 x $$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{3}-2 x^{2}-7 x-4=0 $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$ f(x)=(x-1)^{2}-2 $$

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=5 x^{3}+7 x^{2}-x+9$$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. \(f(x)=5 x^{3}+7 x^{2}-x+9\)

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the difference between y and w.

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x \geq 0 $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$ f(x)=(x-1)^{2}+2 $$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{3}-10 x-12=0 $$

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=11 x^{3}-6 x^{2}+x+3$$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. \(f(x)=11 x^{3}-6 x^{2}+x+3\)

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the sum of y and w.

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+2 x<0 $$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{3}-5 x^{2}+17 x-13=0 $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$ f(x)=(x-3)^{2}+2 $$

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=5 x^{4}+7 x^{2}-x+9$$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. \(f(x)=5 x^{4}+7 x^{2}-x+9\)

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each crational function. $$ f(x)=\frac{x}{x+4} $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 2 x^{2}+3 x>0 $$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ 6 x^{3}+25 x^{2}-24 x+5=0 $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$ y-1=(x-3)^{2} $$

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=11 x^{4}-6 x^{2}+x+3$$