Draw y + 14 = x ( x - 4 ) and label all points of intersection with axes.
To begin with, lets rewrite the equation in a way which is easier to understand by making y the subject and multiplying out the brackets:
y = x2 - 4x - 14
this looks significantly easier to understand and is just a quadratic and so will have a parabolic shape (U shape). Next, we need to find any points of intersections with axes as this will help us place our graph in a sketch. Setting x=0 we easily find that it crosses the y axis at -14. Since this equation is not easily factorised, it will be slightly more strenuous to determine if the it crosses the x-axis as we must use the quadratic formula. To save time we can find out if it intersects the x-axis by calculating the determinant:
det = b2 - 4ac
where a, b and c are, in this case, 1, -4 and -14. The value of the determinant tells us if the quadratic crosses the x-axis (has any solutions) and how many times (how many solutions)- if det > 0, two real solutions, if det = 0 there is one recurring solution and if det < 0 there are no solutions. In this case, det > 0 and therefore we know the parabola passes through the x-axis at two points, one on either side of the y axis- we have deduced the shape! Finally, to find the two points of intersection we just substitute in the a, b and c values into the quadratic formula.
