91Ó°ÊÓ

Write each equation in standard form, if it is not already so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ y=4 x^{2}-32 x+63 $$

Write each equation in standard form, if it is not already so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ (x-1)^{2}+(y-3)^{2}=15 $$

Find each product. \(3 x^{-2} y^{2}\left(4 x^{2}+3 y^{-2}\right)\)

Archery. See the illustration below. An arrow shot from the base of a hill follows the parabolic path \(y=-\frac{1}{6} x^{2}+2 x,\) with distances measured in meters. The inclined hill has a slope of \(\frac{1}{3}\) and can therefore be modeled by the equation \(y=\frac{1}{3} x\). Find the coordinates of the point of impact of the arrow and then its distance from the archer. (GRAPH CANNOT COPY)

Geometry. The area of a rectangle is 63 square centimeters, and its perimeter is 32 centimeters. Find the dimensions of the rectangle.

Compare the graphs of \(\frac{x^{2}}{81}-\frac{y^{2}}{64}=1\) and \(\frac{y^{2}}{81}-\frac{x^{2}}{64}=1 .\) Do they have any similarities?

Find each product. \(\left(2 a^{-2}-b^{-2}\right)\left(2 a^{-2}+b^{-2}\right)\)

Write each equation in standard form, if it is not already so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ (x+1)^{2}+(y+1)^{2}=8 $$

Write each equation in standard form, if it is not already so, and graph it. If the graph is a circle, give the coordinates of its center and its radius. If the graph is a parabola, give the coordinates of its vertex. $$ x=-y^{2}+1 $$

Simplify each expression. \(\frac{x^{-2}+y^{-2}}{x^{-2}-y^{-2}}\)