Fill in the blank with one of the words or phrases listed below. \[\begin{array} { l l l } \text { circle } & \text { ellipse } & \text { hyperbola } \\ \text { conic sections } & \text { vertex } & \text { diameter } \\ \text { center } & \text { radius } & \text { nonlinear system of equations } \end{array}\] -Twice a circle's radius is its -----------

A) conic section B) center C) vertex D) diameter A) conic section B) center C) vertex D) diameter

Fill in the blank with one of the words or phrases listed below. \[\begin{array} { l l l } \text { circle } & \text { ellipse } & \text { hyperbola } \\ \text { conic sections } & \text { vertex } & \text { diameter } \\ \text { center } & \text { radius } & \text { nonlinear system of equations } \end{array}\] -The circle, parabola, ellipse, and hyperbola are called the --------

A) nonlinear system of equations B) center C) conic sections D) vertex A) nonlinear system of equations B) center C) conic sections D) vertex

Exam 13: Conic Sections

Graph the system. - $\left\{\begin{array}{r}x-y \leq-1 \\\frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1\end{array}\right.$ $Graph the system. - \left\{\begin{array}{r} x-y \leq-1 \\ \frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1 \end{array}\right.$

(Multiple Choice)

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Question 41

Graph the equation. - $4 y^{2}-9 x^{2}=36$ $Graph the equation. - 4 y^{2}-9 x^{2}=36$

(Multiple Choice)

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Question 42

Graph the system. - $\left\{ \begin{array} { l } y \geq x ^ { 2 } \\y \geq x + 1 \\y \geq - 4 \\x \geq - 5\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } y \geq x ^ { 2 } \\ y \geq x + 1 \\ y \geq - 4 \\ x \geq - 5 \end{array} \right.$

(Multiple Choice)

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Question 43

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - $y=x^{2}+10 x+19$ $Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y=x^{2}+10 x+19$

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Question 44

Solve. -A bridge constructed over a river has a supporting arch in the shape of a parabola. The length of the road over the parabolic arch is 248 feet and the maximum height of the arch is 112 feet. Write the equation of the arch.

(Multiple Choice)

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Question 45

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - $x=(y+3)^{2}-4$ $Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x=(y+3)^{2}-4$

(Multiple Choice)

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Question 46

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - $y^{2}+x^{2}+4 x=0$ $Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y^{2}+x^{2}+4 x=0$

(Multiple Choice)

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Question 47

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = x ^ { 2 } + 4$

(Multiple Choice)

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Question 48

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -Twice a circle's radius is its -----------

(Multiple Choice)

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Question 49

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}y & = x ^ { 2 } - 3 \\x ^ { 2 } + y ^ { 2 } & = 5\end{aligned} \right.$

(Multiple Choice)

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Question 50

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - $x^{2}+y^{2}-12 x-2 y+33=0$ $Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x^{2}+y^{2}-12 x-2 y+33=0$

(Multiple Choice)

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Question 51

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -The circle, parabola, ellipse, and hyperbola are called the --------

(Multiple Choice)

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Question 52

Graph the equation. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

(Multiple Choice)

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Question 53

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $x = - y ^ { 2 } + 15 y + 1$

(Multiple Choice)

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Question 54

Graph the equation. - $\frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

(Multiple Choice)

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Question 55

Find the center and the radius of the circle. - $( x - 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 6$

(Multiple Choice)

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Question 56

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $y = x ^ { 2 } + 3$

(Multiple Choice)

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Question 57

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = 7 x ^ { 2 } - 5 x - 2$

(Multiple Choice)

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Question 58

Solve. -A planet's orbit about the Sun can be described as an ellipse. Consider the Sun as the origin of a rectangular coordinate system. Suppose that the x-intercepts of the elliptical path of the planet are $\pm 139,000,000$ and that the $y$ -intercepts are $\pm 124,000,000$ . Write the equation of the elliptical path of the planet.

(Multiple Choice)

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Question 59

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$ $Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$

(Multiple Choice)

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Question 60

Showing 41 - 60 of 153

Graph the system. - $\left\{\begin{array}{r}x-y \leq-1 \\\frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1\end{array}\right.$ $Graph the system. - \left\{\begin{array}{r} x-y \leq-1 \\ \frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1 \end{array}\right.$

Graph the equation. - $4 y^{2}-9 x^{2}=36$ $Graph the equation. - 4 y^{2}-9 x^{2}=36$

Graph the system. - $\left\{ \begin{array} { l } y \geq x ^ { 2 } \\y \geq x + 1 \\y \geq - 4 \\x \geq - 5\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } y \geq x ^ { 2 } \\ y \geq x + 1 \\ y \geq - 4 \\ x \geq - 5 \end{array} \right.$

Solve. -A bridge constructed over a river has a supporting arch in the shape of a parabola. The length of the road over the parabolic arch is 248 feet and the maximum height of the arch is 112 feet. Write the equation of the arch.

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = x ^ { 2 } + 4$

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -Twice a circle's radius is its -----------

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}y & = x ^ { 2 } - 3 \\x ^ { 2 } + y ^ { 2 } & = 5\end{aligned} \right.$

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -The circle, parabola, ellipse, and hyperbola are called the --------

Graph the equation. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $x = - y ^ { 2 } + 15 y + 1$

Graph the equation. - $\frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

Find the center and the radius of the circle. - $( x - 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 6$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $y = x ^ { 2 } + 3$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = 7 x ^ { 2 } - 5 x - 2$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 13: Conic Sections

Graph the system. - {x−y≤−1y24−x225≤1\left\{\begin{array}{r}x-y \leq-1 \\\frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1\end{array}\right.{x−y≤−14y2​−25x2​≤1​

Graph the equation. - 4y2−9x2=364 y^{2}-9 x^{2}=364y2−9x2=36

Graph the system. - {y≥x2y≥x+1y≥−4x≥−5\left\{ \begin{array} { l } y \geq x ^ { 2 } \\y \geq x + 1 \\y \geq - 4 \\x \geq - 5\end{array} \right.⎩⎨⎧​y≥x2y≥x+1y≥−4x≥−5​

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y=x2+10x+19y=x^{2}+10 x+19y=x2+10x+19

Solve. -A bridge constructed over a river has a supporting arch in the shape of a parabola. The length of the road over the parabolic arch is 248 feet and the maximum height of the arch is 112 feet. Write the equation of the arch.

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x=(y+3)2−4x=(y+3)^{2}-4x=(y+3)2−4

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y2+x2+4x=0y^{2}+x^{2}+4 x=0y2+x2+4x=0

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - y=x2+4y = x ^ { 2 } + 4y=x2+4

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -Twice a circle's radius is its -----------

Solve the nonlinear system of equations for real solutions. - {y=x2−3x2+y2=5\left\{ \begin{aligned}y & = x ^ { 2 } - 3 \\x ^ { 2 } + y ^ { 2 } & = 5\end{aligned} \right.{yx2+y2​=x2−3=5​

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x2+y2−12x−2y+33=0x^{2}+y^{2}-12 x-2 y+33=0x2+y2−12x−2y+33=0

Fill in the blank with one of the words or phrases listed below. circle ellipse hyperbola conic sections vertex diameter center radius nonlinear system of equations -The circle, parabola, ellipse, and hyperbola are called the --------

Graph the equation. - x225+y216=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 125x2​+16y2​=1

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - x=−y2+15y+1x = - y ^ { 2 } + 15 y + 1x=−y2+15y+1

Graph the equation. - (y−1)225−(x+2)29=1\frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 125(y−1)2​−9(x+2)2​=1

Find the center and the radius of the circle. - (x−8)2+(y−10)2=6( x - 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 6(x−8)2+(y−10)2=6

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - y=x2+3y = x ^ { 2 } + 3y=x2+3

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - y=7x2−5x−2y = 7 x ^ { 2 } - 5 x - 2y=7x2−5x−2

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x2+(y−2)2=16x ^ { 2 } + ( y - 2 ) ^ { 2 } = 16x2+(y−2)2=16

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Graph the system. - $\left\{\begin{array}{r}x-y \leq-1 \\\frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1\end{array}\right.$ $Graph the system. - \left\{\begin{array}{r} x-y \leq-1 \\ \frac{y^{2}}{4}-\frac{x^{2}}{25} \leq 1 \end{array}\right.$

Graph the equation. - $4 y^{2}-9 x^{2}=36$ $Graph the equation. - 4 y^{2}-9 x^{2}=36$

Graph the system. - $\left\{ \begin{array} { l } y \geq x ^ { 2 } \\y \geq x + 1 \\y \geq - 4 \\x \geq - 5\end{array} \right.$ $Graph the system. - \left\{ \begin{array} { l } y \geq x ^ { 2 } \\ y \geq x + 1 \\ y \geq - 4 \\ x \geq - 5 \end{array} \right.$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = x ^ { 2 } + 4$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}y & = x ^ { 2 } - 3 \\x ^ { 2 } + y ^ { 2 } & = 5\end{aligned} \right.$

Graph the equation. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ $Graph the equation. - \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $x = - y ^ { 2 } + 15 y + 1$

Graph the equation. - $\frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the equation. - \frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

Find the center and the radius of the circle. - $( x - 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 6$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $y = x ^ { 2 } + 3$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = 7 x ^ { 2 } - 5 x - 2$