Answers to 10 11 and 12 with explanations

9. you did that right.

10.

A. x=4

B. (4,4)

C. (-∞,-∞)

11. you did not do it right and I will screenshot the answer.

Step-by-step explanation:

a graphing calculator helps a bunch with these types of problems. if you dont have one use demos an online graphing calculator.

9514 1404 393

  10. see attached

  11. axis of symmetry: x=4; vertex: (4, 4); domain: all real numbers; range: y ≤ 4

  12. x = -4, -2

Step-by-step explanation:

10. Your graph is substantially correct. (You might do yourself a favor by adding points ±1 either side of the vertex. This will help to make the graph more rounded near the bottom.) The red graph in the attachment is the graph of this function.

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11. The vertex form of this equation is ...

  f(x) = -(x² -8x) -12 = -(x² -8x +16) -12 +16

  f(x) = -(x -4)² +4

This tells you the vertex is (4, 4). The axis of symmetry is the vertical line through the vertex, so is x=4. The domain of all polynomial functions is "all real numbers." This has a maximum at y=4, so the range is y ≤ 4.

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12. The vertex form of this equation is ...

  f(x) = (x +3)² -1

so the vertex is (-3, -1). Points at x = -3 ± 1 will be the x-intercepts, so the solutions to the equation f(x) = 0. The graph of it is the green graph in the attachment.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3