College Algebra
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Which of the following graphs of a quadratic function satisfies the condition given below?
a < 0; b2 - 4ac = 0
a < 0; b2 - 4ac < 0
a > 0; b2 - 4ac > 0
Determine a quadratic function f(x) for the graph given below.
For the following quadratic function, determine the value of c so that it has only one x-intercept.
y = x2 - 16x + c
For the following quadratic function, determine the values of a so that it has no x-intercepts.
y = ax2 - 18x + 13
Find a quadratic function that satisfies the following conditions.
x-intercepts: (4, 0) and (7, 0)
y-intercept: (0, 14)
Find the other zero of the quadratic equation if one of the zeros is 4 given that the vertex of the function is (8, 4).
Find the coordinates of the closest point on the line y = 3x to the point (2, 14). Use the distance formula.
A ball is thrown upward from the roof of a building with an initial velocity of 16 ft/sec. The height of the building is 50 ft. The equation for the height of the ball after t seconds is given as s(t) = -16t2 + 16t + 50. Determine the time when the ball will achieve a maximum height. Also, find the maximum height.
Choose the correct option to fill in the blanks. In the quadratic equation y=a(x - h)2 + k, if a > 0, the graph opens _____.
Choose the correct option to fill in the blanks. The y-coordinate of the vertex of the graph of y = x2 -24x +149 is ____.
Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.h(x) = (x - 11)2 -2
Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.
h(x) = -(1/3)(x +3)2 -12
Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.h(x) = -6(x -7)2 +1
Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.h(x) = x2 + 12x + 11
Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.h(x) = -9x2 + 54x -76
Find out the domain and range for the graph of the given quadratic function.
Find the graph of the quadratic function.
ƒ(x) = (x - 7)2 - 9
Find the graph of the quadratic function.ƒ(x) = (x +7)2 - 9
Consider the quadratic function f(x) = -2x2 + 16x - 14 and graph it. With the aid of the graph, identify the largest open intervals within its domain at which it is increasing and decreasing. Also, determine its x and y-intercepts, axis of symmetry, vertex, domain, and range.
In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x2 - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2011.
In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x2 - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2015.
In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x2 - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2018.
In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x2 - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2020.
In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x2 - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Graph y = A(x) for the years 2011 to 2022 and determine the year in which the number of students who participated is the least.
Sketch the graph of the parabola defined by f(x) = (x + 1)2 - 4 by using its vertex and intercepts. Identify the domain and range based from the drawn graph, and identify the equation for the axis of symmetry.
Sketch the graph of the parabola defined by f(x) = -x2 - 8x - 12 by using its vertex and intercepts. Identify the domain and range based from the drawn graph, and identify the equation for the axis of symmetry.
Find out the equation of the quadratic function using the given graph.
Draw the graph of the given quadratic equation using vertex and intercepts. Also, find the domain and range using a graph and find the equation of the axis of symmetry. f(x) = 13 -(3x -6)2
Graph the parabola defined by f(x) = x2 - 6x + 5 by using its vertex and intercepts. Determine the equation of its axis of symmetry. Also, based on the graph, identify its domain and range.
Graph the parabola defined by f(x) = x2 - 4x - 5 by using its vertex and intercepts. Determine the equation of its axis of symmetry. Also, based on the graph, identify its domain and range.
Graph the parabola defined by f(x) = 4x - x2 + 5 by using its vertex and intercepts. Determine the equation of its axis of symmetry. Also, based on the graph, identify its domain and range.
Graph the parabola defined by f(x) = 4x - x2 - 7 by using its vertex and intercepts. Determine the equation of its axis of symmetry. Also, based on the graph, identify its domain and range.
Draw the graph of the given quadratic equation using vertex and intercepts. Also, find the domain and range using a graph, and find the equation of the axis of symmetry. f(x) = 2(x +1/2)2 +1
Draw the graph of the given quadratic equation using vertex and intercepts. Also, find the domain and range using a graph and find the equation of the axis of symmetry. f(x) +2 = 6(3x -1)2
Sketch the graph of the parabola defined by f(x)= - (x + 4)2 + 9 by using its vertex and intercepts. Identify the domain and range based from the drawn graph, and identify the equation for the axis of symmetry.
Given the equation for parabola f(x) = -3x2 + 12x - 56, determine its minimum or maximum value and the point where it occurs. Identify also its domain and range. Refer to the equation only and not from its graph.
For the given quadratic equation, write down the coordinates of the vertex of the parabola. f(x) = 7(x -5)2 -3
Find a pair of number which has a difference of 22 and will yield a minimum product. Which of the following gives the minimum product?
For the given quadratic equation, write down the coordinates of the vertex of the parabola. f(x) = -(x +2)2 +7
For the given quadratic equation, write down the coordinates of the vertex of the parabola. f(x) = 3x2 -30x +79
For the given quadratic equation, write down the coordinates of the vertex of the parabola. f(x) = -2x2 -4x +3
Find out whether the function has a minimum value or a maximum value without graphing it. Determine the minimum or maximum value and the point where it occurs. Also, find out the domain and range of the function. f(x) = 9x2-54x+83
Find out whether the function has a minimum value or a maximum value without graphing it. Determine the minimum or maximum value and the point where it occurs. Also, find out the domain and range of the function. f(x) = -5x2-70x-236
Find out whether the function has a minimum value or a maximum value without graphing it. Determine the minimum or maximum value and the point where it occurs. Also, find out the domain and range of the function. f(x) = -4x2+24x
Using the following description of the graph of a quadratic function, determine the domain and range. The vertex is (-5, -6) and the parabola opens up.
Using the following description of the graph of a quadratic function, determine the domain and range. Maximum = 8 at x =7
Find out the equation of the parabola in the vertex form for the given condition:(a) Shape of the parabola same as f(x) = 8x2
(b) vertex of the parabola (4, -7)
Find out the equation of the parabola in the vertex form for the given condition:(a) Shape of the parabola same as f(x) = 13x2
(b) vertex of the parabola (-1, -1)
Find out the equation of the parabola in the vertex form for the given condition:(a) Shape of the parabola same as f(x) = -7x2
(b) Maximum = -3 at x = 6
Find out the equation of the parabola in the vertex form for the given condition:(a) Shape of the parabola same as f(x) = 7x2
(b) Minimum = -3 at x = -2
Two numbers add up to 118, and when multiplied, give a product that is a maximum. Solve for this product.
Two numbers have a difference of 30, and when multiplied, give a product that is a minimum. Solve for this product.
Find the equation of parabola passing through (1, 6) and whose vertex is (3, 2) in vertex form.
Find the equation of parabola passing through (5, 11) and whose vertex is (8, -7) in vertex form.