02:59How to Find the Maximum or Minimum Value of a Quadratic Function EasilywikiHow1054views4rank1comments
Multiple ChoiceIdentify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.264views5rank
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+1258views3rank
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+12x469views2rank
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 303views
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 + 4243views
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 - 2279views
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 + 3277views
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-1303views
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 334views
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.178views
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 ____ .234views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 216views
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 - 106217views
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 326views
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?158views
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. January153views
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. October141views
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. December147views
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. August155views
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. May143views
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+1199views
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?604views1comments
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+5293views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 283views
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 257views
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+3297views
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+8317views
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 - 3318views
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 - 3203views
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)^2−1269views
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+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. y−1=(x−3)^2150views
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)^2−1205views
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)^2283views
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 - 4211views
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−3405views
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 - 3166views
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 +1167views
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−10847views
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 + 5226views
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+3272views
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+3243views
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 - 46380views
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−3255views
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^2−2226views
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−1194views
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−3365views
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^2−5x242views
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.268views
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 = 0176views
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 10249views
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 < 0333views
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)258views
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 > 0644views
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)186views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 291views
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 = -2262views
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 398views
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 = 11238views
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?519views
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?191views
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?197views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).426views
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).300views
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.)183views
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?183views
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).271views
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).525views