1.- \( f(x)=4-x^{2} \)

Did you know that the function \( f(x) = 4 - x^2 \) is a classic example of a parabola? It opens downward, with its vertex at the point \( (0, 4) \). This means the highest point on this graph is 4, making it a perfect illustration of how quadratic functions can model real-life scenarios, such as projectile motion! In terms of problem-solving, a common mistake with this quadratic function is neglecting to identify its intercepts. To find the x-intercepts, set \( f(x) = 0 \), leading to the equation \( 4 - x^2 = 0 \). Solving this reveals the intercepts at \( x = -2 \) and \( x = 2 \), so don't skip that step!