Provide step by step solution for all the questions given below please

2. Determine the vertex of a quadratic function satisfying the following: - Is congruent to y = -2x2 - 10 - Passes through (1, 36) and (-5, 12) - Has no x- intercept 133. a) Sketch a quadratic function that satisfies the following Passes through the point (a, 0), a>0 Has a maximum value Has an axis of symmetry given by the equation x + b = 0, b > 0 13 b) State the coordinates of the second x-intercept. 4. If f(x) = 3x2 - 18x - 3 and g(x) = x2 - 18x - 3 a) Determine the positive difference in the minimum values of f (x) and g (x). b) State the transformation applied to g (x) so that it will have the same vertex as f (x ). /45. Determine algebraically the range of y = -2(x - 3)2 - 7x. 13 6. Two objects are launched in the same direction but at different angles from the top of a 42m high building. Both objects reach a maximum height of 56m. At their maximum height, the horizontal distances travelled by the two objects are 8m and 16m. How far apart do the two objects strike the ground? 147. Determine the maximum area of a rectangle that has a base on the x-axis and upper vertices on the lines y = 12 - x and y = 12 + x where y