Consider the quadratic polynomial P(x)=2x2−5x−3.
(i) Define a zero of a polynomial and explain how it is represented on the graph of y=P(x).
(ii) Verify that x=3 and x=−21 are zeros of P(x).
(iii) State the coordinates of the x-intercepts and the y-intercept of the graph of y=P(x).
(iv) Describe whether the parabola opens upwards or downwards and draw a rough, clearly labelled sketch showing only the intercepts found in part (iii).