Function: y=−x2+3x+8𝑦=−𝑥2+3𝑥+8Vertex: (( ,, ))Solutions: (( , )) and (( ,, )

The function you provided is a quadratic function in the form of y = ax^2 + bx + c, where a = -1, b = 3, and c = 8.

1. To find the vertex of the parabola, we use the formula h = -b/2a. Here, b = 3 and a = -1. So, h = -3/(-2) = 1.5. To find the y-coordinate of the vertex, we substitute h into the equation: k = -(1.5)^2 + 3*1.5 + 8 = -2.25 + 4.5 + 8 = 10.25. So, the vertex of the parabola is (1.5, 10.25).

2. To find the solutions or roots of the equation, we set y = 0 and solve for x. This gives us the equation -x^2 + 3x + 8 = 0. We can solve this equation by factoring, completing the square, or using the quadratic formula. Here, we'll use the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a). This gives us x = [-3 ± sqrt((3)^2 - 4*(-1)8)] / (2-1) = [-3 ± sqrt(9 + 32)] / -2 = [-3 ± sqrt(41)] / -2. So, the solutions are x = (3 - sqrt(41)) / -2 and x = (3 + sqrt(41)) / -2.