Chapter 12

Find the domain and the range of the function. $$f(x)=\sqrt{x-8}$$

Solve the equation. $$x^{2}-6 x+1=0$$

MULTIPLE CHOICE What term should you add to \(x^{2}-\frac{1}{2} x\) so that the result is a perfect square trinomial? $$\begin{array}{ccccc}\mathbf{A} &\frac{1}{2} & \mathbf{B} & \frac{1}{4} & \mathbf{C} & \frac{1}{16} & \mathbf{D} &\frac{1}{32}\end{array}$$

Two numbers have a geometric mean of \(12 .\) One number is 32 more than the other. Find the numbers.

Find the domain and the range of the function. $$f(x)=\sqrt{\frac{1}{2} x^{2}}$$

Solve the equation. $$x^{2}+3 x-10=0$$

MULTIPLE CHOICE Solve \(x^{2}+8 x-2=0\) $$\begin{array}{ccccc}\mathbf{A})-4 \pm 3 \sqrt{2} & \mathbf{B} & 4 \pm 3 \sqrt{2} & \mathbf{C} & -4 \pm 2 \sqrt{2} & \mathbf{D} & \mathbf{4} \pm \sqrt{\mathbf{1 6}} \end{array}$$

Find the domain and the range of the function. $$f(x)=\sqrt{x}+4$$

Solve the equation. $$2 x^{2}+x=3$$

VERTEX FORM The vertex form of a quadratic function is \(y=a(x-h)^{2}+k\). Its graph is a parabola with vertex at \((\boldsymbol{h}, \boldsymbol{k})\). Use completing the square to write the quadratic function in vertex form. Then give the coordinates of the vertex of the graph of the function. $$y=x^{2}+10 x+25$$

Find the domain and the range of the function. $$f(x)=6 x$$

Solve the equation. $$4 x^{2}-6 x+1=0$$

VERTEX FORM The vertex form of a quadratic function is \(y=a(x-h)^{2}+k\). Its graph is a parabola with vertex at \((\boldsymbol{h}, \boldsymbol{k})\). Use completing the square to write the quadratic function in vertex form. Then give the coordinates of the vertex of the graph of the function. $$y=2 x^{2}+12 x+13$$

Find the domain and the range of the function. $$f(x)=\sqrt{x+3}$$

Find the product. $$(x-2)(x+11)$$

VERTEX FORM The vertex form of a quadratic function is \(y=a(x-h)^{2}+k\). Its graph is a parabola with vertex at \((\boldsymbol{h}, \boldsymbol{k})\). Use completing the square to write the quadratic function in vertex form. Then give the coordinates of the vertex of the graph of the function. $$y=-x^{2}-5 x+6$$

Find the product. $$(x+4)(3 x-7)$$

Explain why the quadratic formula gives solutions only if \(a \neq 0\) and \(b^{2}-4 a c \geq 0\).

Using \(4 \sqrt{x}=2 x+k,\) find three different expressions that can be substituted for \(k\) so that the equation has two solutions, one solution, and no solution. Describe how you found the equations.

Find the product. $$(2 x-3)(5 x-9)$$

Find the mean, the median, and the mode of the collection of numbers. $$1,5,2,4,3,6,1$$

Solve the equation. $$x^{2}=36$$

Find the product. $$(x-5)(x-4)$$

Find the mean, the median, and the mode of the collection of numbers. $$9,6,10,14,10,3$$

Solve the equation. $$x^{2}=11$$

Find the product. $$(6 x+2)\left(x^{2}-x-1\right)$$

Find the mean, the median, and the mode of the collection of numbers. $$-6,20,-8,-18,10$$

Solve the equation. $$7 x^{2}=700$$

Find the product. $$(2 x-1)\left(x^{2}+x+1\right)$$

Find the mean, the median, and the mode of the collection of numbers. $$17,9,11,15,4,15,8,3,11$$

Solve the equation. $$25 x^{2}-9=-5$$

Simplify the expression. $$\frac{8 x}{3} \cdot \frac{1}{x}$$

Solve the linear system. $$\begin{array}{l}y=4 x \\\x+y=10\end{array}$$

Solve the equation. $$\frac{1}{7} x^{2}-7=-7$$

Simplify the expression. $$\frac{8 x^{2}}{3} \cdot \frac{9}{16 x}$$

Solve the linear system. $$\begin{aligned}&3 x+y=12\\\&9 x-y=36\end{aligned}$$

Solve the equation. $$-16 t^{2}+48=0$$

Simplify the expression. $$\frac{x}{x+6} \div \frac{x+1}{x+6}$$

Solve the linear system. $$\begin{aligned}&2 x-y=8\\\&2 x+2 y=2\end{aligned}$$

Multiply. $$(x+5)^{2}$$

Four American Presidents' faces are carved on Mount Rushmore: Washington, Jefferson, Roosevelt, and Lincoln. Before the faces were carved on the cliff, scale models were made. The ratio of the faces on the cliff to the models was 12 to \(1 .\) If the scale model of President Washington's face was 5 feet tall, how tall is his face on Mount Rushmore?

Solve the equation. $$16+x^{2}=64$$

Multiply. $$(2 x-3)^{2}$$

Solve the equation. $$x^{2}+81=144$$

Multiply. $$(3 x+5 y)(3 x-5 y)$$

Solve the equation. $$x^{2}+25=81$$

Multiply. $$(6 y-4)(6 y+4)$$

Solve the equation. $$4 x^{2}-144=0$$

Multiply. $$(x+7 y)^{2}$$

Solve the equation. $$x^{2}-30=-3$$