Question

Identify the key features of the parabola that is formed by the equation

Answer 1

Answer:

• y-intercept: 58
• vertex: (2, 78) -- a maximum

Step-by-step explanation:

The negative leading coefficient tells you this parabola opens downward, so the vertex will be a maximum. The constant is the y-intercept, which is 58.

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The vertex is nicely found using a graphing calculator, but can also be found algebraically. The x-value is ...

  x = -b/(2a) = -19.8/(2·(-4.9)) = 19.8/9.8 = 99/49 ≈ 2.02041

The value of f(99/49) is ...

  f(99/49) = (-4.9(99/49) +19.8)(99/49) +58 = (9.9)(99/49) +58 ≈ 78.002

The location of the vertex is approximately ...

  (x, y) ≈ (2.0204, 78.002) ≈ (2, 78)