Algebra
Answer the following for the given quadratic function. f(x) = x2 + 4x - 12 Does the graph of f open up or down? Up Down What is the vertex (h,k) of f? (h,k) = (Simplify your answer. Type an ordered pair.) Graph f(x) = 2x2 - 3x + 4 by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept and x-intercepts, if any. Determine the domain and the range of the function. Determine where the function is increasing and where it is decreasing. The graph opens up. What are the coordinates of the vertex? (Type an ordered pair. Use integers or fractions for any numbers in the expression. Simplify your answer.) The price p and the quantity x sold of a certain product obey the demand equation p = - 1/4x + 90, 0 le x le 360 Express the revenue R as a function of x. What is the revenue if 196 units are sold? What quantity x maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue? Express the revenue R as a function of x. R(x) = The rate of a chemical reaction varies, depending on the initial amount of a certain compound. In general the reaction rate, V, can be expressed by the following formula, where k is a positive constant, and a is the initial amount of the compound. V(x) = kx(a - x) The positive constant, k, for one such reaction is 0.7, and the initial amount of the compound, a, is 8. For what value of x is the rate a maximum? The rate is a maximum when x is .
Show transcribed image text Answer the following for the given quadratic function. f(x) = x2 + 4x - 12 Does the graph of f open up or down? Up Down What is the vertex (h,k) of f? (h,k) = (Simplify your answer. Type an ordered pair.) Graph f(x) = 2x2 - 3x + 4 by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept and x-intercepts, if any. Determine the domain and the range of the function. Determine where the function is increasing and where it is decreasing. The graph opens up. What are the coordinates of the vertex? (Type an ordered pair. Use integers or fractions for any numbers in the expression. Simplify your answer.) The price p and the quantity x sold of a certain product obey the demand equation p = - 1/4x + 90, 0 le x le 360 Express the revenue R as a function of x. What is the revenue if 196 units are sold? What quantity x maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue? Express the revenue R as a function of x. R(x) = The rate of a chemical reaction varies, depending on the initial amount of a certain compound. In general the reaction rate, V, can be expressed by the following formula, where k is a positive constant, and a is the initial amount of the compound. V(x) = kx(a - x) The positive constant, k, for one such reaction is 0.7, and the initial amount of the compound, a, is 8. For what value of x is the rate a maximum? The rate is a maximum when x is .