Graph the parabola by hand, and check using a graphing calculator: Give the vertex, axis, domain, and range.

$$y=(x+3)^2-4$$

Graph the parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range.

$$x=-2(y+3)^2$$

In this exercise, you will evaluate the composite function

Let $f(x)=\sqrt{x}$ and $g(x)=x^2-1$. Evaluate the expression given below.

$$g(f(0))$$

A solid S is generated by revolving the region between the x-axis and the curve y=

$$\sqrt { \sin x } ( 0 \leq x \leq \pi )$$

about the x-axis. An integral expression for the volume of S is ___.

Find the surface area of the solid generated by revolving each curve about the x-axis. $x(t)=3 t^{2}$, $y(t)=6 t$; $0 \leq t \leq 1$

Find the area of the surface obtained by revolving the curve x=sin t, y=cos 2t, for $-\pi / 4 \leq t \leq \pi / 4$, about the x-axis.

Find the area of the surface generated by revolving the curve about (a) the x-axis and (b) the y-axis. x = 2 cos θ, y = 2 sin θ, 0 ≤ θ ≤ π/2

In this exercise, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.

$$y=2x^2, y=0, x=2$$

the line $x=2$

Find all vertical asymptotes. $f(x)=\frac{x^{2}+1}{x^{3}+3 x^{2}+2 x}$

Identify the condition in the following diagnoses.
Bullous keratopathy, left eye
main term: __________

Write in the blank whether the sentence is simple or compound.

Lauren is sweeping the dugout, and Kat is cleaning the bases.

Graph the parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range.

$$x=y^2+2 y-8$$

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the y-axis. $y=\frac{x^{2}}{2}+4$, $0 \leq x \leq 2$

Let C be the curve x = f(t), y = g(t), for $a \leq t \leq b$, where f' and g' are continuous on[a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is $s=\int_{a}^{b} 2 \pi g(t) \sqrt{f^{\prime}(t)^{2}+g^{\prime}(t)^{2}} d t$. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is $S=\int_{a}^{b} 2 \pi f(t) \sqrt{f^{\prime}(t)^{2}+g^{\prime}(t)^{2}} d t$. Find the area of the surface obtained by revolving the curve $x=\cos ^{3} t, y=\sin ^{3} t$, for $0 \leq t \leq \pi / 2$, about the x-axis.