11 (a) If x² + 4x - 3 = (x + a)² + b for all possible values of x, find a and b.

(b) If y = x² + 4x - 3 , state the minimum value of y, and the value of x at which this minimum occurs.

(c) Sketch the graph of y = x² + 4x - 3 .
Try to use your answer to part (a) to calculate the co-ordinates of all intersections with the axes.

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?