Evaluate Quadratic Functions Question Given \( f(x)=-x^{2}-3 x+20 \), find \( f(5) \) \( \begin{array}{l}\text { Answer } \\ \begin{array}{l}\text { Attemptiout of } 2\end{array} \\ \square\end{array} \)

To find \( f(5) \) for the function \( f(x)=-x^{2}-3x+20 \), we substitute \( x \) with \( 5 \): \[ f(5) = -(5)^{2} - 3(5) + 20 \] Calculating step-by-step: \[ f(5) = -25 - 15 + 20 = -25 - 15 + 20 = -20 \] So, \( f(5) = -20 \). When evaluating quadratic functions like this one, always remember to follow the order of operations: first handle the exponent, then multiplication, and finally addition or subtraction. A common mistake is forgetting to apply the negative sign in front of the squared term, which can lead to incorrect results. Always double-check your steps to avoid these pitfalls! Quadratics have fascinating real-world applications, from calculating projectile motion to maximizing profits in businesses. For instance, when determining the optimal height and angle for a cannonball's trajectory, the path of the ball can be modeled by a quadratic function. Understanding how these functions behave can help in making informed decisions in various fields!