7. Sketch the graph of f(x) = 2(x - 1.5)2 + 3, then state the domain and range of the function (show all your work). (4 points)
8. Determine the value of a given that (7, 6) satisfies the quadratic function f(x) = a(x – 5)2 +6. (Show all your
work). (2 points)

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  7. D: (-∞, ∞); R: [3, ∞); see attached for a graph (red)

  8. a=0; see attached for a graph

Step-by-step explanation:

7. The function is a polynomial, so its domain is all real numbers.

The parabola opens upward. It has a minimum value of 3. The range is y ≥ 3.

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8. Putting the given point coordinates in the equation, we can solve for a.

  f(7) = 6

  6 = a(7 -5)² +6

  0 = a(2²)

  0 = a

The value of a is zero.

(The given point has the same y-value as the vertex, but is not the vertex. The function can only go through that point if it is a horizontal line (not a parabola).) The attachment shows a graph.