02:59How to Find the Maximum or Minimum Value of a Quadratic Function EasilywikiHow1067views4rank1comments
Multiple ChoiceIdentify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.270views5rank
Multiple ChoiceGraph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. f(x)=−(x−5)2+1f\left(x\right)=-\left(x-5\right)^2+1f(x)=−(x−5)2+1267views3rank
Multiple ChoiceGraph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. f(x)=3x2+12xf\left(x\right)=3x^2+12xf(x)=3x2+12x483views2rank
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 311views
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = - (x + 1)^2 + 4246views
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = (x + 4)^2 - 2286views
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = -x^2 +2x + 3284views
Textbook QuestionGraph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x^2-12x-1316views
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 345views
Textbook QuestionFill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.185views
Textbook QuestionFill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .239views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 221views
Textbook QuestionIn Exercises 5–6, use the function's equation, and not its graph, to find (a) the minimum or maximum value and where it occurs. (b) the function's domain and its range. f(x) = -x^2 + 14x - 106220views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 333views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. Sketch a graph of y=V(x) for January through December. In what month are the fewest volunteers available?160views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. January156views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. October143views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. December148views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. August159views
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. May146views
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2(x−3)^2+1204views
Textbook QuestionAmong all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?612views1comments
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−2(x+1)^2+5296views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 292views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 263views
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x^2−8x+3302views
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−x^2−2x+8324views
Textbook QuestionMatch each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)^2 - 3325views
Textbook QuestionMatch each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x + 4)^2 - 3206views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=(x−4)^2−1274views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=(x−1)^2+2148views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. y−1=(x−3)^2153views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2(x+2)^2−1206views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=4−(x−1)^2290views
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = (x - 5)^2 - 4214views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2−2x−3416views
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -1/2 (x + 1)^2 - 3175views
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3 (x - 2)^2 +1170views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2+3x−10856views
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = x^2 + 6x + 5232views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x^2+3274views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2+6x+3244views
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3x^2 + 24x - 46391views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x^2+4x−3259views
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x^2−2230views
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=3x^2−12x−1198views
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=−4x^2+8x−3374views
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=5x^2−5x249views
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. The vertex is and the parabola opens up.272views
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b^2 - 4ac = 0180views
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 10256views
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; ^b2 - 4ac < 0339views
Textbook QuestionIn Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (5, 3)262views
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0661views
Textbook QuestionIn Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (−10, −5)189views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 298views
Textbook QuestionIn Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Maximum = 4 at x = -2267views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 408views
Textbook QuestionIn Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Minimum = 0 at x = 11241views
Textbook QuestionAmong all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is the maximum product?534views
Textbook QuestionAmong all pairs of numbers whose difference is 24, find a pair whose product is as small as possible. What is the minimum product?194views
Textbook QuestionHeight of an Object If an object is projected upward from an initial height of 100 ft with an initial velocity of 64 ft per sec, then its height in feet after t seconds is given by s(t) = -16t^2 + 64t + 100. Find the number of seconds it will take the object to reach its maximum height. What is this maximum height?200views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).434views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).305views
Textbook QuestionThe distance between the two points P(x₁, y₁) and R(x₂, y₂) is d(P, R) = √(x₁ - x₂)^2 + (y₁ -y₂)^2. Distance formula. Find the closest point on the line y = 2x to the point (1, 7). (Hint: Every point on y = 2x has the form (x, 2x), and the closest point has the minimum distance.)185views
Textbook QuestionA quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?188views
Textbook QuestionIn Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).278views
Textbook QuestionIn Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).535views