It can be shown that for the quadratic function f(x) = ax²+bx+c, the x-coordinate of -b the parabola's vertex will always be x = - 2a For each function below, -b ● Use the vertex formula x = to determine the x-coordinate of the parabola's 2a vertex. (Show your work!) Evaluate a in order to determine the y-coordinate of the vertex. (Show your 2a work!) ● Graph f(x) on your calculator to verify that the coordinates of the vertex that you found are correct. 1. f(x)=3x²-12x+7 - f(x)=-2x²-12x-10 5 f(x) = x² 3 2 4

a) Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.) Vertex:  (−2, −11);   point:  (0, −3)   b) Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.) Vertex: (−7, −2);   point:  (−8, 0)

O For the force field F = (2xe¬y, (2y – x²e=y)) in some open connected region containing P(1, 0) and Q(2, 1) O Confirm that F is conservative O Find a potential function o O Find the work done by the force F acting on a particle from P to Q.

Determine and correctly interpret the maximum or minimum of the quadratic functions that model the following situations using valid mathematical procedures and the correct mathematical notation. Express your answer in terms of the context of the problem. A fireworks rocket is launched from a platform. Its height h, in meters, above the ground after t seconds is given by the function h(t) = –9t^2 + 100t + 35. a. What is the maximum height reached by the projectile?b. How long did it take to reach the maximum height?