Evaluate the expression $p^2+5 p-8$ when $p=-3$.
The given expression is \(p^2 + 5p - 8\), and we are asked to evaluate it when the variable \(p\) is equal to \(-3\). To solve this, we will perform a direct substitution of the value \(p = -3\) into the expression and then follow the order of operations to determine the final result.
We substitute \(p = -3\) into the expression \(p^2 + 5p - 8\):
\((-3)^2 + 5(-3) - 8\)
First, calculate the square:
\((-3)^2 = 9\)
Next, calculate the product:
\(5 \times (-3) = -15\)
Finally, combine these values:
\(9 - 15 - 8\)
Calculating the final sum:
\(9 - 15 = -6\)
\(-6 - 8 = -14\)
The final result of the expression when \(p = -3\) is \(-14\). Comparing this with the provided options, the correct choice is \(-14\). Thus, the value of the expression is \(\boxed{-14}\).
This type of algebraic substitution is frequently used in computer programming when you need to calculate values based on user input or sensor data. For example, if a program models the vertical position of an object dropped from a certain height using a quadratic equation like \(h(t) = at^2 + bt + c\), you would substitute the time \(t\) into the equation to find the object's height at any given moment. Mastering this skill ensures you can accurately compute outcomes in various dynamic systems.