By drawing the graphs of y=x+3 and y=5−x on the same Cartesian plane, find the solution to the simultaneous equations.

An incomplete table of values for the function y=x2−2x−3 is given. Complete the table. | x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---|---|---| | y | 5 | | -3| | -3| | 5 |

Draw the graph of the function y=x2−2x−3 for the domain −2≤x≤4.

From the graph of y=x2−2x−3, write down the coordinates of the turning point.

From the graph, find the minimum value of the function y=x2−2x−3.

Write the equation of the axis of symmetry for the graph of y=x2−2x−3.

Using your graph, find the roots of the equation x2−2x−3=0.

Find the interval of values of x for which the function y=x2−2x−3 is negative.

Find the interval of values of x for which the function y=x2−2x−3 is increasing.

Draw the graph of the function y=5−x−x2 for the domain −4≤x≤3.

From the graph of y=5−x−x2, find its maximum value.

Without drawing the graph, write the equation of the axis of symmetry and the coordinates of the turning point of the function y=(x−3)2+4.

Without drawing the graph, state whether the function y=−(x+1)(x−5) has a maximum or a minimum value and find the x-coordinates of the points where it intersects the x-axis.

Using the graph of y=x2−2x−3, find the roots of the equation x2−2x−5=0.

A person buys 3 pens and 2 books for Rs. 130. Another person buys 2 pens and 3 books for Rs. 120. Construct a pair of simultaneous equations and solve them graphically to find the price of a pen and a book.