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Find the values of b such that the function has the given maximum value [tex]f(x) = -x^2+bx-65[/tex]. I already have it in vertex form as [tex]-(x+\frac{b}{2})^2-65+\frac{b^2}{4}[/tex] but I don't know what to do from here

Sagot :

Mhanifaidn

Answer:

  • b = {20, -20}

Step-by-step explanation:

Given function:

  • f(x) = -x² + bx - 65 with maximum value of 35

To find

  • The value of b

Solution:

Maximum value is obtained at vertex as a < 0

Vertex coordinate of x is:

  • x = -b/2a = -b / -2 = 1/2b

Solving for b:

  • 35 = - (1/2b)² + b(1/2b) - 65
  • - 1/4b² + 1/2b² = 100
  • 1/4b² = 100
  • b² = 400
  • b = √400
  • b = ± 20

See attached

View image Mhanifa
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