Consider the function [math: f(x)=a(x+2)2(x−1)]. If the graph of the function passes through the point [math: (0,12)], find the value of [math: a].单项选择题
A
A. [math: −3]
B
B. [math: 3]
C
C. [math: −2]
D
D. [math: 2]
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Which of the following mathematical functions, used in predictive analytical models, is represented by the formula y = ax3 + bx2 + cx + d?
Which of the equations given below would be a possible equation to describe this curve?
问题文本和以前一样，请通过填空的方式回答下列问题。 不要使用空格，如果答案不是整数，请用斜杠表示分数（例如 1/2 或 5/4）。 用途 - 用于任何负面情况。 __________________________________________________________________________________________________________________________________此题8分。以下问题与函数 , 有关。[math: f:(−∞,2]→R][math: f(x)=3x3−5x2−4x+4] a) 如果的一个因子，这意味着 ([math: (x+1)][math: f(x)][math: f]回答问题 1 问题 2[input])。[math: =0] b) 将 除以。 [math: f(x)][math: (x+1)]商 是 回答问题 2[input][math: x2] [math: −] 问题 2 的答案 3[input][math: x] [math: +] 问题 2 的答案 4[input]。 c) 多项式 可以 完全 分解 为：[math: f(x)][math: f(x)=(x+1)] ( 回答问题 2 的第 5 题[input][math: x] [math: −] 问题 2 的答案 6[input])( [math: x−] 问题 2 的答案 7[input] ） d) 使用图形计算器求的 范围， 将任何十进制近似值 四舍五入 到小数点后两位。 [math: f(x)]取值范围为[math: f(x)∈(−∞,] 问题 2 的答案 8[input] [math: ]]
Part 1Graph the polynomial function f(x)equals=(xplus+22)cubed3(xminus−77) using parts (a) through (e). Part 1(a) Determine the end behavior of the graph of the function.The graph of f behaves like yequals=[input]x Superscript 4x4 for large values of StartAbsoluteValue x EndAbsoluteValuex.Part 2(b) Find the x- and y-intercepts of the graph of the function.The x-intercept(s) is/are [input]negative 2,7−2,7 .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)Part 3The y-intercept is [input]negative 56−56 . (Simplify your answer. Type an integer or a fraction.)Part 4(c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.The real zero(s) of f is/are [input]negative 2,7−2,7 .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)Part 5The lesser zero is a zero of multiplicity [input]33 , so the graph of f [input] crosses Your answer is correct. You answered crosses. the x-axis at xequals=[input]negative 2−2 . The greater zero is a zero of multiplicity [input]11 , so the graph of f [input] crosses Your answer is correct. You answered crosses. the x-axis at xequals=[input]77 . Part 6(d) Determine the maximum number of turning points on the graph of the function.[input]33 (Type a whole number.) Part 7(e) Use the information to draw a complete graph of the function. Choose the correct graph. A. -1010-700700xy Edit coordinates (0,0) A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 700 to 700 in increments of 70. From left to right, a curve falls first steeply and then shallowly passing through the point (negative 2, 0) before falling steeply through (0, negative 56) to a minimum at (5,negative 692), then rises through (7, 0). All coordinates are approximate. B. -1010-700700xy Edit coordinates (0,0) A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 700 to 700 in increments of 70. From left to right, a curve rises steeply through the point (negative 7, 0) to a maximum at (negative 5,692), then falls first steeply then shallowly through (0, 56) to the point (2, 0) before falling steeply again. All coordinates are approximate. C. -1010-700700xy Edit coordinates (0,0) A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 700 to 700 in increments of 70. From left to right, a curve rises first steeply and then shallowly passing through the point (negative 2, 0) before rising steeply through (0, 56) to a maximum at (5,692), then falling through (7, 0). All coordinates are approximate. D. -1010-700700xy Edit coordinates (0,0) A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 700 to 700 in increments of 70. From left to right, a curve falls steeply through the point (negative 7, 0) to a minimum at (negative 5,negative 692), then rises first steeply then shallowly through (0, negative 56) to the point (2, 0) before rising steeply again. All coordinates are approximate.
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