Chapter 9.4, Problem 43E

To determine

To determine whether the quadratic function has maximum or minimum value the find that value .

Answer to Problem 43E

The function has maximum value.

Maximum value is -5

Explanation of Solution

Given:

Equation:

  $y=-x^2-10x-30$

Concept Used:

Maximum or minimum value of the function

Calculation:

On comparing the equation $a{x}^2+bx+c$ ,

  $a=-1,b=-10,c=-30$

Since , $a<0$

The function has maximum value.

For maximum value,

Calculate $x$

  $x=\frac{-b}{2a}$

Therefore ,

  $x=\frac{-(-10)}{2(-1)}$

So,

= $x=\frac{10}{-2}$

On substituting $x=-5$ in equation.

  $y=-{(-5)}^2-10(-5)-30$

On solving,

  $y=-25+50-30$

Therefore ,

  $y=-5$