Find the values of b such that the

Answered question

2022-03-29

Find the values of b such that the function has the given maximum value.

Maximum value: 62

f(x) = −x2 + bx − 19 

 

b =            (smaller value)

b =           (larger value)

Answer & Explanation

user_27qwe

user_27qwe

Skilled2022-04-21Added 375 answers

f(x)=-x2+bx-19

The maximum of a quadratic function occurs at x=-b2a. If aa is negative, the maximum value of the function is f(-b2a).

fmaxx=ax2+bx+c occurs at x=-b2a

Find the value of x=-b2a.

Substitute in the values of aa and bb.

x=-12(-1)

Remove parentheses.

x=-12(-1)

Simplify -12(-1).

x=12

Evaluate f(12).

Replace the variable x with 12 in the expression.

f(12)=-(12)2+b(12)-19

Simplify the result.

Simplify each term.

f(12)=-14+b2-19

To write -19 as a fraction with a common denominator, multiply by 44.

f(12)=b2-14-1944

Combine -19 and 44.

f(12)=b2-14+-1944

Combine the numerators over the common denominator.

f(12)=b2+-1-1944

Simplify the numerator.

Tap for more steps...

f(12)=b2+-774

Move the negative in front of the fraction.

f(12)=b2-774

The final answer is b2-774.

b2-774

Use the x and y values to find where the maximum occurs.

(12,b2,-774)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?