91Ó°ÊÓ

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=-2(x+3)^{2}+2$$

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=\frac{2}{3}(x-2)^{2}-1$$

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=x^{2}-2 x+3$$

Sound Detection Microphones are placed at points \((-c, 0)\) and \((c, 0) .\) An explosion occurs at point \(P(x, y)\) having positive \(x\) -coordinate. The sound is detected at the closer microphone \(t\) seconds before being detected at the farther microphone. Assume that sound travels at a speed of 330 meters per second, and show that \(P\) must be on the hyperbola $$ \frac{x^{2}}{330^{2} t^{2}}-\frac{y^{2}}{4 c^{2}-330^{2} t^{2}}=\frac{1}{4} $$ (GRAPH CANT COPY)

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=x^{2}+6 x+5$$

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=2 x^{2}-4 x+5$$

Equation of a Hyperbola Suppose a hyperbola has center at the origin, foci at \(F^{\prime}(-c, 0)\) and \(F(c, 0),\) and equation $$ \left|d\left(P, F^{\prime}\right)-d(P, F)\right|=2 a $$ Let \(b^{2}=c^{2}-a^{2},\) and show that the points on the hyperbola satisfy the equation $$ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $$

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$y=-3 x^{2}+24 x-46$$

Equation of an Ellipse Use the definition of an ellipse to find an equation of an ellipse with foci \((3,0)\) and \((-3,0),\) where the sum of the distances from any point of the ellipse to the two foci is \(10 .\)

Graph each parabola by hand, and check using a graphing calculator. Give the vertex, axis, domain, and range. $$x=y^{2}+2$$