Draw the graph of y=x^2-4x-21

We know that this is going to be a “U” shaped parabola as the graph is a positive x^2 graph. The y intercept is the point at which x=0. Substituting in 0 gives when x = 0, y = -21.Now we need the x intercepts, so we need the values of x when y=0x^2-4x-21=0Therefore to factorise we need 2 numbers which sum to -4 and when multiplied together are -21. Therefore(x+3)(x-7)=0x+3=0 or x-7=0 therefore when y=0, x=-3 or +7, so these are our x intercepts.Finally we need the vertex.We want the equation in the form (x+b)^2+cTo find b and c, complete the square (x^2+2ax+a^2)-4x=2ax therefore a=-2x^2-4x+4-21=4x^2-4x+4=25(x-2)^2=25(x-2)^2-25=yThis is therefore a translation of the graph of y=x^2 with the vertex at (2,-25), so this is a “U” shaped parabola with the following coordinates marked and labelled: (-3,0), (7,0), (0,-21), (2,-25)