Find a power function that models the data in the table. Round to three decimal places if necessary. -The table lists the amount of emissions of a certain pollutant in millions of tons. $\begin{array}{r|rrrr} \text { Year } & 1980 & 1985 & 1990 & 1995 \\ \hline \mathrm{P} & 18.8 & 22.6 & 26.0 & 29.0 \end{array}$ If the amount of emissions is modeled by a function of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { ax } { } ^ { 2 } + b x + c$ where $x$ is the year, estimate th amount of emissions in the year $2025 .$

A) 43.8 million tons B) 38.6 million tons C) 34.0 million tons D) 41.7 million tons A) 43.8 million tons B) 38.6 million tons C) 34.0 million tons D) 41.7 million tons

Exam 3: Quadratic, Piecewise-Defined, and Power Functions

The function defined by $D ( t ) = 13 t ^ { 2 } -$ 73t gives the distance in feet that a car going approximately 50 mph will skid in t seconds. Find the time it would take for the car to skid 380 ft. Round to the nearest tenth.

(Multiple Choice)

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Question 181

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=x^{2}-2 x-6$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=x^{2}-2 x-6$

(Multiple Choice)

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Question 182

Determine if the graph of the function is concave up or concave down - $y = - \frac { 2 } { 5 } ( x + 5 ) ^ { 2 } - 4$

(Multiple Choice)

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Question 183

Determine if the graph of the function is concave up or concave down - $y = x ^ { 2 } - 4 x + 4$

(Multiple Choice)

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Question 184

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=2 x^{2}-12 x+22$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2 x^{2}-12 x+22$

(Multiple Choice)

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Question 185

The manager of big box store has found that if the price of a pillow is $\mathrm { p } ( \mathrm { x } ) = 95 - \frac { \mathrm { x } } { 8 }$ , then $\mathrm { x }$ pillows will be sold. The expression for the total revenue from the sale of $x$ pillows is $R ( x ) = 95 x - \frac { x ^ { 2 } } { 8 }$ . Find the number of pillows that will produce maximum revenue.

(Multiple Choice)

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Question 186

Solve the equation. - $| 5 m + 3 | = 9$

(Multiple Choice)

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Question 187

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 4 / 9 }$

(Multiple Choice)

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Question 188

Find a power function that models the data in the table. Round to three decimal places if necessary. -The table lists the amount of emissions of a certain pollutant in millions of tons. Year 1980 1985 1990 1995 18.8 22.6 26.0 29.0 If the amount of emissions is modeled by a function of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { ax } { } ^ { 2 } + b x + c$ where $x$ is the year, estimate th amount of emissions in the year $2025 .$

(Multiple Choice)

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Question 189

Use factoring to solve the equation - $25 k ^ { 2 } - 4 = 0$

(Multiple Choice)

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Question 190

If a ball is thrown upward at 19.6 meters per second from the top of a building that is 70 meters high, the height of the ball can be modeled by $S = 70 + 19.6 t - 4.9 t ^ { 2 }$ meters, where t is the number of seconds after the ball is Thrown. What is the ball's maximum height?

(Multiple Choice)

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Question 191

Find the exact solutions to the quadratic equation in the complex numbers. - $( x - 9 ) ^ { 2 } = - 16$

(Multiple Choice)

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Question 192

Write a quadratic equation that is most easily solved using the principle of square roots. Explain why the principle of zero products would not work as easily on the equation you wrote.

(Essay)

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Question 193

Use the quadratic formula to - $x ^ { 2 } - x = 20$

(Multiple Choice)

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Question 194

Find the function value. -For $f ( x ) = | x - 9 |$ , find $f ( 5 )$ .

(Multiple Choice)

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Question 195

Write the equation of the quadratic function whose graph is a parabola containing the given points. -An egg is dropped from the top of a 1600-foot-high building. The ball is 1456 feet above the ground after 3 seconds, and it reaches level ground in 10 seconds. The height above the ground is a quadratic function of the Time after the ball is thrown. Write the equation of this function.

(Multiple Choice)

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Question 196

Use the graph of the function to estimate the x-intercepts. - $y=-x^{2}+2 x+35$ $Use the graph of the function to estimate the x-intercepts. - y=-x^{2}+2 x+35$

(Multiple Choice)

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Question 197

Solve the equation by completing the square. - $2 m ^ { 2 } + 12 m + 5 = 0$

(Multiple Choice)

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Question 198

$x ^ { 2 } - \frac { 6 } { 5 } x = - \frac { 7 } { 10 }$

(Multiple Choice)

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Question 199

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 2 ) , \left( 1 , \frac { 4 } { 3 } \right) , ( - 3 , - 8 )$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 261

The function defined by $D ( t ) = 13 t ^ { 2 } -$ 73t gives the distance in feet that a car going approximately 50 mph will skid in t seconds. Find the time it would take for the car to skid 380 ft. Round to the nearest tenth.

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=x^{2}-2 x-6$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=x^{2}-2 x-6$

Determine if the graph of the function is concave up or concave down - $y = - \frac { 2 } { 5 } ( x + 5 ) ^ { 2 } - 4$

Determine if the graph of the function is concave up or concave down - $y = x ^ { 2 } - 4 x + 4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=2 x^{2}-12 x+22$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2 x^{2}-12 x+22$

Solve the equation. - $| 5 m + 3 | = 9$

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 4 / 9 }$

Use factoring to solve the equation - $25 k ^ { 2 } - 4 = 0$

If a ball is thrown upward at 19.6 meters per second from the top of a building that is 70 meters high, the height of the ball can be modeled by $S = 70 + 19.6 t - 4.9 t ^ { 2 }$ meters, where t is the number of seconds after the ball is Thrown. What is the ball's maximum height?

Find the exact solutions to the quadratic equation in the complex numbers. - $( x - 9 ) ^ { 2 } = - 16$

Write a quadratic equation that is most easily solved using the principle of square roots. Explain why the principle of zero products would not work as easily on the equation you wrote.

Use the quadratic formula to - $x ^ { 2 } - x = 20$

Find the function value. -For $f ( x ) = | x - 9 |$ , find $f ( 5 )$ .

Use the graph of the function to estimate the x-intercepts. - $y=-x^{2}+2 x+35$ $Use the graph of the function to estimate the x-intercepts. - y=-x^{2}+2 x+35$

Solve the equation by completing the square. - $2 m ^ { 2 } + 12 m + 5 = 0$

$x ^ { 2 } - \frac { 6 } { 5 } x = - \frac { 7 } { 10 }$

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 2 ) , \left( 1 , \frac { 4 } { 3 } \right) , ( - 3 , - 8 )$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

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Exam 3: Quadratic, Piecewise-Defined, and Power Functions

The function defined by D(t)=13t2−D ( t ) = 13 t ^ { 2 } -D(t)=13t2− 73t gives the distance in feet that a car going approximately 50 mph will skid in t seconds. Find the time it would take for the car to skid 380 ft. Round to the nearest tenth.

Graph the quadratic equation on [ [−10,10] by [−10,10][ - 10,10 ] \text { by } [ - 10,10 ][−10,10] by [−10,10] oes this window give a complete graph? - f(x)=x2−2x−6f(x)=x^{2}-2 x-6f(x)=x2−2x−6

Determine if the graph of the function is concave up or concave down - y=−25(x+5)2−4y = - \frac { 2 } { 5 } ( x + 5 ) ^ { 2 } - 4y=−52​(x+5)2−4

Determine if the graph of the function is concave up or concave down - y=x2−4x+4y = x ^ { 2 } - 4 x + 4y=x2−4x+4

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2x2−12x+22y=2 x^{2}-12 x+22y=2x2−12x+22

Solve the equation. - ∣5m+3∣=9| 5 m + 3 | = 9∣5m+3∣=9

Determine if the function is concave up or concave down in the first quadrant. - y=x4/9y = x ^ { 4 / 9 }y=x4/9

Use factoring to solve the equation - 25k2−4=025 k ^ { 2 } - 4 = 025k2−4=0

Find the exact solutions to the quadratic equation in the complex numbers. - (x−9)2=−16( x - 9 ) ^ { 2 } = - 16(x−9)2=−16

Write a quadratic equation that is most easily solved using the principle of square roots. Explain why the principle of zero products would not work as easily on the equation you wrote.

Use the quadratic formula to - x2−x=20x ^ { 2 } - x = 20x2−x=20

Find the function value. -For f(x)=∣x−9∣f ( x ) = | x - 9 |f(x)=∣x−9∣ , find f(5)f ( 5 )f(5) .

Use the graph of the function to estimate the x-intercepts. - y=−x2+2x+35y=-x^{2}+2 x+35y=−x2+2x+35

Solve the equation by completing the square. - 2m2+12m+5=02 m ^ { 2 } + 12 m + 5 = 02m2+12m+5=0

x2−65x=−710x ^ { 2 } - \frac { 6 } { 5 } x = - \frac { 7 } { 10 }x2−56​x=−107​

Write the equation of the quadratic function whose graph is a parabola containing the given points. - (0,−2),(1,43),(−3,−8)( 0 , - 2 ) , \left( 1 , \frac { 4 } { 3 } \right) , ( - 3 , - 8 )(0,−2),(1,34​),(−3,−8)

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

The function defined by $D ( t ) = 13 t ^ { 2 } -$ 73t gives the distance in feet that a car going approximately 50 mph will skid in t seconds. Find the time it would take for the car to skid 380 ft. Round to the nearest tenth.

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=x^{2}-2 x-6$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=x^{2}-2 x-6$

Determine if the graph of the function is concave up or concave down - $y = - \frac { 2 } { 5 } ( x + 5 ) ^ { 2 } - 4$

Determine if the graph of the function is concave up or concave down - $y = x ^ { 2 } - 4 x + 4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=2 x^{2}-12 x+22$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2 x^{2}-12 x+22$

Solve the equation. - $| 5 m + 3 | = 9$

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 4 / 9 }$

Use factoring to solve the equation - $25 k ^ { 2 } - 4 = 0$

Find the exact solutions to the quadratic equation in the complex numbers. - $( x - 9 ) ^ { 2 } = - 16$

Use the quadratic formula to - $x ^ { 2 } - x = 20$

Find the function value. -For $f ( x ) = | x - 9 |$ , find $f ( 5 )$ .

Use the graph of the function to estimate the x-intercepts. - $y=-x^{2}+2 x+35$ $Use the graph of the function to estimate the x-intercepts. - y=-x^{2}+2 x+35$

Solve the equation by completing the square. - $2 m ^ { 2 } + 12 m + 5 = 0$

$x ^ { 2 } - \frac { 6 } { 5 } x = - \frac { 7 } { 10 }$

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 2 ) , \left( 1 , \frac { 4 } { 3 } \right) , ( - 3 , - 8 )$