Calculate g(-3) for g(x) = x² + 5x - 11.

Understand the Problem

The question is asking us to find the value of the function g(x) when x is equal to -3. To solve this, we will substitute -3 into the equation g(x) = x² + 5x - 11 and simplify the expression.

Answer

$g(-3) = -17$

Steps to Solve

Substituting the value into the function

We start by substituting $x = -3$ into the function $g(x) = x^2 + 5x - 11$.

$$ g(-3) = (-3)^2 + 5(-3) - 11 $$

Calculating the squared term

Calculate the square of $-3$:

$$ (-3)^2 = 9 $$

So now, we have:

$$ g(-3) = 9 + 5(-3) - 11 $$

Calculating the multiplication

Next, calculate $5 \times -3$:

$$ 5(-3) = -15 $$

Now, substitute this back into the equation:

$$ g(-3) = 9 - 15 - 11 $$

Performing the final calculations

Now we simplify the expression step-by-step:

First, simplify $9 - 15$:

$$ 9 - 15 = -6 $$

Then subtract $11$:

$$ -6 - 11 = -17 $$

Thus, we find that:

$$ g(-3) = -17 $$

The value of the function when $x = -3$ is $g(-3) = -17$.

More Information

This problem involves substituting a value into a quadratic function and performing basic arithmetic calculations. Quadratic functions often model real-world situations, such as projectile motion and area calculations.

Tips

Forgetting the order of operations: Always perform squaring before addition or subtraction.
Miscalculating negative values: Be careful with signs when working with negative numbers.

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