Evaluate Quadratic Functions Question Examples Given \( f(x)=-4 x^{2}+7 x \), find \( f(5) \) Answer Attempt 1 out ©f 2 Sidbmit Anewer

To evaluate the quadratic function \( f(x)=-4 x^{2}+7 x \) at \( x=5 \), simply substitute 5 into the function. This gives you: \[ f(5) = -4(5)^{2} + 7(5) = -4(25) + 35 = -100 + 35 = -65. \] So, \( f(5) = -65 \)! Quadratic functions have a wide array of real-world applications, from calculating trajectories of objects in motion to optimizing profit margins in business models. For example, businesses can use quadratic equations to determine the price at which they should sell a product for maximum profit, integrating variables like cost and demand. When dealing with quadratic functions, a common mistake is neglecting to consider the vertex or the axis of symmetry, which can reveal crucial information about the function's maximum or minimum value. Ensure to find the vertex using the formula \( x = -\frac{b}{2a} \) if optimizing a scenario or just sketching the graph for better understanding.