Find the values of b such that the function has the given maximum value f(x) = -x^2+bx-65. I already have it in vertex form as -(x+(b)/(2))^2-65+(b^2)/(4) but I don't know …

Question

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

Answer 1

• b = {20, -20}

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