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Which quadratic inequality includes all values less than those represented by a quadratic function with a vertex of (5, –3) and containing the point (0, –8)? y is less-than-or-equal-to one-third (x 3) squared 5 y less-than negative one-fifth (x 5) squared minus 3 y less-than-or-equal-to 13 over 9 (x minus 3) squared 5 y less-than negative one-fifth (x minus 5) squared minus 3



Answer :

sqdancefan

Answer:

  (d)  y < -1/5(x -5)² -3

Step-by-step explanation:

You want the inequality describing values less than the quadratic function through point (0, -8) with vertex (5, -3).

Vertex form

The vertex form of a quadratic function is ...

  f(x) = a(x -h)² +k . . . . . . . scale factor 'a' and vertex (h, k)

For the given point and vertex, we can find 'a' from ...

  -8 = a(0 -5)² -3

  -5 = 25a

  a = -5/25 = -1/5

Then we have ...

  f(x) = -1/5(x -5)² -3

Inequality

The inequality representing values less than f(x) is ...

  y < -1/5(x -5)² -3 . . . . . . matches choice D

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