Chapter 5

Graph each function. $$ y=3(x+3)^{2} $$

Find the exact solutions by using the Quadratic Formula. \(8 x^{2}+18 x-5=0\)

Solve each equation by using the Square Root Property. \(x^{2}+14 x+49=9\)

Simplify. $$ \sqrt{56} $$

Write a quadratic equation with the given root(s). Write the equation in standard form. \(-4,7\)

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

Graph each inequality. $$ y < x^{2}-16 $$

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

Find the exact solutions by using the Quadratic Formula. \(x^{2}+8 x=0\)

Solve each equation by using the Square Root Property. \(x^{2}-12 x+36=25\)

Simplify. $$ \sqrt{80} $$

Write a quadratic equation with the given root(s). Write the equation in standard form. \(\frac{1}{2}, \frac{4}{3}\)

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

Graph each inequality. $$ y > -2 x^{2}-4 x+3 $$

Graph each function. $$ y=-2 x^{2}+16 x-31 $$

Find the exact solutions by using the Quadratic Formula. \(4 x^{2}+4 x+1=0\)

Solve each equation by using the Square Root Property. \(x^{2}+16 x+64=7\)

Simplify. $$ \sqrt{\frac{48}{49}} $$

Write a quadratic equation with the given root(s). Write the equation in standard form. \(-\frac{3}{5},-\frac{1}{3}\)

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. $$ f(x)=-x^{2}+4 x-1 $$

Graph each inequality. $$ y \leq-x^{2}+5 x+6 $$

Which function has the widest graph? $$ \begin{array}{lllll}{\text { A } y=-4 x^{2}} & {\text { B } y=-1.2 x^{2}} & {\text { C } y=3.1 x^{2}} & {\text { D } y=11 x^{2}}\end{array} $$

Find the exact solutions by using the Quadratic Formula. \(x^{2}+6 x+9=0\)

Solve each equation by using the Square Root Property. \(9 x^{2}-24 x+16=2\)

Simplify. $$ \sqrt{\frac{120}{9}} $$

Factor each polynomial. \(x^{3}-27\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -x^{2}-7 x=0 $$

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

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=5(x+3)^{2}-1 $$

Find the exact solutions by using the Quadratic Formula. \(2 x^{2}-4 x+1=0\)

The height \(h\) of an object \(t\) seconds after it is dropped is given by \(h=-\frac{1}{2} g t^{2}+h_{0},\) where \(h_{0}\) is the initial height and \(g\) is the acceleration due to gravity. The acceleration due to gravity near Earth's surface is \(9.8 \mathrm{m} / \mathrm{s}^{2},\) while on Jupiter it is 23.1 \(\mathrm{m} / \mathrm{s}^{2} .\) Suppose an object is dropped from an initial height of 100 meters from the surface of each planet. On which planet should the object reach the ground first?

Simplify. $$ \sqrt{-36} $$

Factor each polynomial. \(4 x y^{2}-16 x\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ x^{2}-2 x-24=0 $$

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. $$ f(x)=2 x^{2}-4 x+1 $$

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}-6 x-7<0 $$

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

Find the exact solutions by using the Quadratic Formula. \(x^{2}-2 x-2=0\)

The height \(h\) of an object \(t\) seconds after it is dropped is given by \(h=-\frac{1}{2} g t^{2}+h_{0},\) where \(h_{0}\) is the initial height and \(g\) is the acceleration due to gravity. The acceleration due to gravity near Earth's surface is \(9.8 \mathrm{m} / \mathrm{s}^{2},\) while on Jupiter it is 23.1 \(\mathrm{m} / \mathrm{s}^{2} .\) Suppose an object is dropped from an initial height of 100 meters from the surface of each planet. Find the time it takes for the object to reach the ground on each planet to the nearest tenth of a second.

Factor each polynomial. \(3 x^{2}+8 x+5\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 25+x^{2}+10 x=0 $$

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. $$ f(x)=3 x^{2}+10 x $$

Solve each inequality using a graph, a table, or algebraically. $$ x^{2}-x-12>0 $$

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=-3 x^{2}-18 x+11 $$

Find the exact solutions by using the Quadratic Formula. \(x^{2}+3 x+8=5\)

Simplify. $$ (6 i)(-2 i) $$

The height \(h\) of an object \(t\) seconds after it is dropped is given by \(h=-\frac{1}{2} g t^{2}+h_{0},\) where \(h_{0}\) is the initial height and \(g\) is the acceleration due to gravity. The acceleration due to gravity near Earth's surface is \(9.8 \mathrm{m} / \mathrm{s}^{2},\) while on Jupiter it is 23.1 \(\mathrm{m} / \mathrm{s}^{2} .\) Suppose an object is dropped from an initial height of 100 meters from the surface of each planet. Do the times to reach the ground seem reasonable? Explain.

Solve each equation by factoring. Then graph. \(x^{2}-11 x=0\)

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ -14 x+x^{2}+49=0 $$

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=-x^{2}+7 $$