A parabola cuts the x-axis at (−3,0) and at (p,0). Its axis of symmetry is the line x=1 and its vertex lies on the horizontal line y=−4.
(i) Determine the value of p.
(ii) Write the quadratic polynomial in factored form with an unknown leading coefficient a.
(iii) Using the vertex information, find the value of a and hence obtain the polynomial in standard form.
(iv) Verify that the vertex satisfies the polynomial obtained and clearly state the coordinates of all intercepts and the vertex.