91Ó°ÊÓ

The coordinates of a point in the uv-coordinate system are given. Find the coordinates of the point in the \(x y\) -coordinate system, which has been rotated \(\theta\) radians from the \(x y-\)coordinate system. $$(-3,1), \theta=\frac{\pi}{3}$$

Write the equation of the function \(f(x)\) that is obtained by shifting the graph of \(g(x)=x^{2}\) to the left 3 units.

Complete the square. $$y^{2}+8 y$$

Identify the conic section given by each of the equations. $$r=\frac{3}{1+6 \sin \theta}$$

Write the equation of the function \(f(x)\) that is obtained by shifting the graph of \(g(x)=x^{2}\) to the right 1 unit.

The coordinates of a point in the uv-coordinate system are given. Find the coordinates of the point in the \(x y\) -coordinate system, which has been rotated \(\theta\) radians from the \(x y-\)coordinate system. $$(-2,4), \theta=\frac{\pi}{6}$$

Sketch the graph of the parametric equations. Indicate the direction of increasing \(t\). $$x=-t, \quad y=t^{2}+1,-1 \leq t \leq 2$$

Sketch the graph of the parametric equations. Indicate the direction of increasing \(t\). $$x=t, \quad y=3 t^{2}-1,-3 \leq t \leq 3$$

Identify the conic section given by each of the equations. $$r=\frac{1}{1+0.75 \cos \theta}$$

The coordinates of a point in the uv-coordinate system are given. Find the coordinates of the point in the \(x y\) -coordinate system, which has been rotated \(\theta\) radians from the \(x y-\)coordinate system. $$(-1,-2), \theta=\frac{\pi}{6}$$