solve for the following

\f\f\fdetermine the following properties: a) direction of opening b) y-intercept c) zeros d) equation of the axis of symmetry e) vertex f) optimal value g) domain h) rangeFor the following quadratic function: f (20 ) = NO /CO x - 5 a) Rewrite the equation to vertex form using the completing the square method. [4] b) State the coordinates of the vertex, the equation of the axis of symmetry, and the optimal value. [2] c) State two ways the domain can be restricted so that the inverse of the quadratic is a function. [1] d) Determine the equation of the inverse of the quadratic. [3]A sportswear store sells baseball caps with the Toronto Raptor's logo on them. Last year. the store sold 600 caps at $30. The store manager is planning to increase the price. A consumer survey shows that for every $2.50 increase, there will be a drop of 20 sales a year. The store is supplied the baseball caps from the manufacturer at a cost of $19 for each cap. a) What is the annual maximum profit from the baseball caps? b) What should the selling price be to maximize the annual profit? c) How many baseball caps need to be sold to maximize annual profit? Given the graph of the quadratic function\f3) Determine the range if the domain is restricted to 10