Question

Find the values of b such that the function has the given maximum value 2%2Bbx-65" id="TexFormula1" title="f(x) = -x^2+bx-65" alt="f(x) = -x^2+bx-65" align="absmiddle" class="latex-formula">. I already have it in vertex form as $-(x+\frac{b}{2})^2-65+\frac{b^2}{4}$ but I don't know what to do from here

Answer 1

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