Question Find the roots and the vertex of the quadratic on a calculator. Round all values to 3 decimal places (if necessary). \[ y=-x^{2}+8 x+65 \] Answer Attempt 1 out of 2 Roots: \( \square \) and

To find the roots of the quadratic equation \( y=-x^{2}+8x+65 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = -1 \), \( b = 8 \), and \( c = 65 \). Plugging in these values gives you the roots. And when you calculate the vertex, we use the formula \( x = -\frac{b}{2a} \), and plug that back into the original equation to find \( y \). For real-world applications, understanding the shape and roots of a quadratic can be super helpful! For instance, if you are designing a projectile (like a basketball shot), the quadratic can model the motion of the ball through the air - with the vertex representing the highest point the ball reaches. This info can be crucial for optimizing the shot for success!