Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. -\[\begin{array} { l } f ( x ) = x ^ { 2 } - 13 x + 36 \\ g ( x ) = 2 x ^ { 2 } - 16 x + 32 \\ \end{array}\]

A) $x=-\frac{\sqrt{32}}{2}, x=\frac{\sqrt{32}}{2}$ B) $x = 4 , x = - 1$ C) $x = \frac { 1 } { 4 } , x = - 1$ D) $x = - \frac { \sqrt { 17 } } { 2 } , x = \frac { \sqrt { 17 } } { 2 }$ A) $x=-\frac{\sqrt{32}}{2}, x=\frac{\sqrt{32}}{2}$ B) $x = 4 , x = - 1$ C) $x = \frac { 1 } { 4 } , x = - 1$ D) $x = - \frac { \sqrt { 17 } } { 2 } , x = \frac { \sqrt { 17 } } { 2 }$

Exam 2: Linear and Quadratic Functions

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$ . During what interval of time will the rocket be higher than $147 \mathrm {~m}$ ?

(Multiple Choice)

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Question 161

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). - $f(x)=-x^{2}+1$ $Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). - f(x)=-x^{2}+1$

(Multiple Choice)

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Question 162

Solve the problem. -Alan is building a garden shaped like a rectangle with a semicircle attached to one short side along its diameter. The diameter of the semicircle is equal to the width of the short side of the rectangle. If he has 30 feet of fencing to go around the garden, what dimensions will give him the maximum area in the garden?

(Multiple Choice)

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Question 163

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = - x ^ { 2 } - 10 x$

(Multiple Choice)

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Question 164

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=-13x+36 g(x)=2-16x+32

(Multiple Choice)

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Question 165

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } - 6 x$

(Multiple Choice)

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Question 166

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}+4 x+3$ $Graph the function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}+4 x+3$

(Multiple Choice)

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Question 167

Determine if the type of relation is linear, nonlinear, or none. -

(Multiple Choice)

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Question 168

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$

(Multiple Choice)

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Question 169

Find the zeros of the quadratic function using the Square Root Method. List the x-intercepts of the graph of the function. - $f ( x ) = x ^ { 2 } - 49$

(Multiple Choice)

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Question 170

Solve the equation. - $| 6 x | = 3$

(Multiple Choice)

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Question 171

Determine the slope and y-intercept of the function. -f(x) = 2x + 11

(Multiple Choice)

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Question 172

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 12 x$

(Multiple Choice)

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Question 173

Solve the problem. -An object is propelled vertically upward from the top of a 128-foot building. The quadratic function models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. $s ( t ) = - 16 t ^ { 2 } + 112 t + 128$ How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if Necessary.

(Multiple Choice)

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Question 174

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 10 t ^ { 2 } + 320 t$ After how many seconds does it reach its maximum height?

(Multiple Choice)

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Question 175

Solve the problem. -The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $30 for the repairman to come to the house, to which a charge of $23 per hour is added. Find an equation that Can be used to determine the labor cost, C(x), of a repair that takes x hours.

(Multiple Choice)

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Question 176

Solve the problem. -Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 3 Miles.

(Multiple Choice)

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Question 177

Use the slope and y-intercept to graph the linear function. - $\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$ $Use the slope and y-intercept to graph the linear function. - \mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$

(Multiple Choice)

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Question 178

Write the word or phrase that best completes each statement or answers the question. -The following table shows the median number of hours of leisure time that Americans had each week in various years. Year 1973 1980 1987 1993 1997 Median \# of Leisure hrs per Week 26.2 19.2 16.6 18.8 19.5 Use x = 0 to represent the year 1973. Using a graphing utility, determine the quadratic regression equation for the data given. What year corresponds to the time when Americans had the least time to spend on leisure?

(Short Answer)

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Question 179

Determine the domain and the range of the function. - $f ( x ) = - x ^ { 2 } + 2 x$

(Multiple Choice)

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Question 180

Showing 161 - 180 of 302

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$ . During what interval of time will the rocket be higher than $147 \mathrm {~m}$ ?

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = - x ^ { 2 } - 10 x$

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=-13x+36 g(x)=2-16x+32

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } - 6 x$

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}+4 x+3$ $Graph the function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}+4 x+3$

Determine if the type of relation is linear, nonlinear, or none. -

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$

Find the zeros of the quadratic function using the Square Root Method. List the x-intercepts of the graph of the function. - $f ( x ) = x ^ { 2 } - 49$

Solve the equation. - $| 6 x | = 3$

Determine the slope and y-intercept of the function. -f(x) = 2x + 11

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 12 x$

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 10 t ^ { 2 } + 320 t$ After how many seconds does it reach its maximum height?

Solve the problem. -Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 3 Miles.

Use the slope and y-intercept to graph the linear function. - $\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$ $Use the slope and y-intercept to graph the linear function. - \mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$

Determine the domain and the range of the function. - $f ( x ) = - x ^ { 2 } + 2 x$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 2: Linear and Quadratic Functions

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after ttt seconds is given by h=−9.8t2+78.4th = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }h=−9.8t2+78.4t . During what interval of time will the rocket be higher than 147 m147 \mathrm {~m}147 m ?

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). - f(x)=−x2+1f(x)=-x^{2}+1f(x)=−x2+1

Find the vertex and axis of symmetry of the graph of the function. - f(x)=−x2−10xf ( x ) = - x ^ { 2 } - 10 xf(x)=−x2−10x

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=-13x+36 g(x)=2-16x+32

Find the vertex and axis of symmetry of the graph of the function. - f(x)=x2−6xf ( x ) = x ^ { 2 } - 6 xf(x)=x2−6x

Graph the function using its vertex, axis of symmetry, and intercepts. - f(x)=x2+4x+3f(x)=x^{2}+4 x+3f(x)=x2+4x+3

Determine if the type of relation is linear, nonlinear, or none. -

Find the real zeros of the function. List the x-intercepts of the graph of the function. - Q(x)=(−5x+4)2−2(−5x+4)−24Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24Q(x)=(−5x+4)2−2(−5x+4)−24

Find the zeros of the quadratic function using the Square Root Method. List the x-intercepts of the graph of the function. - f(x)=x2−49f ( x ) = x ^ { 2 } - 49f(x)=x2−49

Solve the equation. - ∣6x∣=3| 6 x | = 3∣6x∣=3

Determine the slope and y-intercept of the function. -f(x) = 2x + 11

Determine the domain and the range of the function. - f(x)=x2+12xf ( x ) = x ^ { 2 } + 12 xf(x)=x2+12x

Solve the problem. -A projectile is thrown upward so that its distance above the ground after ttt seconds is h=−10t2+320th = - 10 t ^ { 2 } + 320 th=−10t2+320t After how many seconds does it reach its maximum height?

Solve the problem. -Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 3 Miles.

Use the slope and y-intercept to graph the linear function. - F(x)=16x\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }F(x)=61​x

Determine the domain and the range of the function. - f(x)=−x2+2xf ( x ) = - x ^ { 2 } + 2 xf(x)=−x2+2x

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$ . During what interval of time will the rocket be higher than $147 \mathrm {~m}$ ?

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = - x ^ { 2 } - 10 x$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } - 6 x$

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}+4 x+3$ $Graph the function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}+4 x+3$

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$

Find the zeros of the quadratic function using the Square Root Method. List the x-intercepts of the graph of the function. - $f ( x ) = x ^ { 2 } - 49$

Solve the equation. - $| 6 x | = 3$

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 12 x$

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 10 t ^ { 2 } + 320 t$ After how many seconds does it reach its maximum height?

Use the slope and y-intercept to graph the linear function. - $\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$ $Use the slope and y-intercept to graph the linear function. - \mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$

Determine the domain and the range of the function. - $f ( x ) = - x ^ { 2 } + 2 x$