Chapter 6.8, Problem 68S

To determine

To calculate: The value of the expression $g\left(-3\right)$ where $g\left(x\right)=-4x^2$ .

Answer to Problem 68S

The value of the expression $g\left(-3\right)$ is $-36$ .

Explanation of Solution

Given information:

The function $g\left(x\right)=-4x^2$ and value of xas $-3$ .

Formula used:

To evaluate an algebraic expression that involves variables, substitute the corresponding values of variables and simplify.

When there is more than one operation in an expression, follow the steps below to evaluate the expression,

Step 1: Evaluate the expression inside the parenthesis.

Step 2: Evaluate the expression that involves power.

Step 3: Multiply or divide the expression from left to right.

Step 4: Add or subtract the expression from left to right.

Calculation:

Consider the function $g\left(x\right)=-4x^2$ and value of xas $-3$ .

Substitute x as $-3$ in the above expression,

  $g\left(-3\right)=-4{\left(-3\right)}^2$

Recall that when there is more than one operation in an expression, follow the steps below to evaluate the expression,

Step 1: Evaluate the expression inside the parenthesis.

Step 2: Evaluate the expression that involves power.

Step 3: Multiply or divide the expression from left to right.

Step 4: Add or subtract the expression from left to right.

Apply it, recall that the expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Use $-3$ as a base 2 times,

  $\begin{array}{c}g\left(-3\right)=-4{\left(-3\right)}^2\\ =-4\left(9\right)\\ =-36\end{array}$

Thus, the value of the expression $g\left(-3\right)$ is $-36$ .