02:59How to Find the Maximum or Minimum Value of a Quadratic Function EasilywikiHow990views4rank1comments
Multiple ChoiceIdentify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.247views4rank
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+1238views1rank
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+12x423views1rank
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 291views
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 + 4236views
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 - 2265views
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 + 3264views
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-1271views
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 306views
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.173views
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 ____ .220views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 200views
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 - 106211views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 310views
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?151views
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. January145views
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. October138views
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. December145views
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. August151views
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. May137views
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+1196views
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?583views1comments
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+5281views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 265views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 245views
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+3281views
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+8299views
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 - 3299views
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 - 3193views
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)^2−1254views
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+2138views
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)^2145views
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)^2−1197views
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)^2274views
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 - 4201views
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−3384views
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 - 3159views
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 +1159views
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−10801views
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 + 5217views
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+3263views
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+3235views
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 - 46342views
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−3242views
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^2−2216views
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−1188views
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−3348views
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^2−5x232views
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.256views
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 = 0167views
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 10233views
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 < 0320views
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)247views
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 > 0603views
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)177views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 273views
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 = -2251views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 365views
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 = 11222views
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?496views
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?186views
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?194views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).401views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).279views
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.)176views
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?172views
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).256views
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).498views