Chapter 10

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation. Then find the length of the latus rectum and graph the parabola. $$ y=x^{2}+4 x $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ 9 x^{2}+4 y^{2}-24 y=0 $$

Each equation is of the form \(A x^{2}+B x y+C y^{2}+D x+\) \(E y+F=0 .\) Identify the values of \(A, B,\) and \(C\). $$ -3 x^{2}+x y+2 y^{2}+4 x-7 y=0 $$

Write an equation of the hyperbola that satisfies each set of conditions. vertices \((6,-6)\) and \((0,-6),\) foci \((3 \pm \sqrt{13},-6)\)

Simplify each radical expression. \(\sqrt{25}\)

Find the midpoint of the line segment with endpoints having the given coordinates. $$ (5,-7),(3,-1) $$

Find the coordinates of the vertices and foci and the equations of the asymptotes of the hyperbola with the equation \(6 y^{2}-2 x^{2}=24 .\) Then graph the hyperbola. ( \(\operatorname{lossn} 105\) )

Each equation is of the form \(A x^{2}+B x y+C y^{2}+D x+\) \(E y+F=0 .\) Identify the values of \(A, B,\) and \(C\). $$ x^{2}-4 x+4 y+2=0 $$

Find the coordinates of the center and foci and the lengths of the major and minor axes of the ellipse with equation \(4 x^{2}+9 y^{2}-24 x+72 y+144=0\)Then graph the ellipse.

Simplify each radical expression. \(\sqrt{81}\)

Find the midpoint of the line segment with endpoints having the given coordinates. $$ (2,-9),(-4,5) $$

Each equation is of the form \(A x^{2}+B x y+C y^{2}+D x+\) \(E y+F=0 .\) Identify the values of \(A, B,\) and \(C\). $$ -x y-2 x-3 y+6=0 $$

Simplify. Assume that no variable equals 0 \(\left(x^{3}\right)^{4}\)

Simplify each radical expression. \(\sqrt{144}\)

Find the midpoint of the line segment with endpoints having the given coordinates. $$ (8,0),(-5,12) $$

Simplify. Assume that no variable equals 0 \(\left(m^{5} n^{-3}\right)^{2} m^{2} n^{7}\)

Simplify each radical expression. \(\sqrt{12}\)

Find all of the rational zeros for each function. $$ f(x)=x^{3}+5 x^{2}+2 x-8 $$

Simplify. Assume that no variable equals 0 $$ \frac{x^{2} y^{-3}}{x^{-5} y} $$

Simplify each radical expression. \(\sqrt{18}\)

Find all of the rational zeros for each function. $$ g(x)=2 x^{3}-9 x^{2}+7 x+6 $$

HEAIH The prediction equation \(y=205-0.5 x\) relates a person's maximum heart rate for exercise \(y\) and age \(x\) . Use the equation to find the maximum heart rate for an 18 -year old.

Simplify each radical expression. \(\sqrt{48}\)

The perimeter of a rectangular picture is 86 inches. Twice the width exceeds the length by 2 inches. What are the dimensions of the picture?

Simplify each radical expression. \(\sqrt{72}\)

Solve each equation. Assume that all variables are positive. $$ c^{2}=13^{2}-5^{2} $$

Solve each equation. Assume that all variables are positive. $$ c^{2}=10^{2}-8^{2} $$

PREREQUISITE SKILL Solve each system of equations. $$ \begin{array}{l}{y=x+4} \\ {2 x+y=10}\end{array} $$

Solve each equation. Assume that all variables are positive. $$ (\sqrt{7})^{2}=a^{2}-3^{2} $$

PREREQUISITE SKILL Solve each system of equations. $$ \begin{array}{l}{4 x+y=14} \\ {4 x-y=10}\end{array} $$

Solve each equation. Assume that all variables are positive. $$ 4^{2}=6^{2}-b^{2} $$

PREREQUISITE SKILL Solve each system of equations. $$ \begin{array}{l}{x+5 y=10} \\ {3 x-2 y=-4}\end{array} $$