Write the equation of a quadratic function with the given solutions. Use standard forr \( f(x)=a x^{2}+b x+c \). \( x=12 \) and \( x=5 \)

To create a quadratic function from the given solutions \( x = 12 \) and \( x = 5 \), we can start by using the factored form of a quadratic equation. The roots lead us to: \( f(x) = a(x - 12)(x - 5) \) Expanding this gives: \( f(x) = a(x^2 - 17x + 60) \) To put it in standard form, we can simply choose \( a = 1 \) for simplicity: \( f(x) = x^2 - 17x + 60 \) Now we have the equation of the quadratic function! Fun fact: Quadratic equations can describe a wide variety of real-world situations, such as the trajectory of a ball thrown in the air! The parabolic shape of the graph illustrates the way gravity affects its path, creating a beautiful arc. Need a hand with quadratic equations in your daily life? Whether you’re calculating the optimal dimensions for a garden or figuring out the perfect angle to launch a projectile, mastering quadratics can help you solve practical problems. Just remember to double-check your factoring or use the quadratic formula for those stubborn equations!