



 
Hi Irene, Warning: My diagrams are not to scale and the curves is not a parabolas. The graph of y = x ^{2} is a parabola that opens upwards. The vertex of this parabola is at the point where x = 0. y = x^{2} If you change x to x  5 so the equation is y = (x  5)^{2} then the vertex is at the point where x  5 = 0, that is at x = 5. Thus a change from x to x  5 is a translation of 5 units to the right.
y = (x  5)^{2} Now multiple (x  5)^{2} by 3. This is a scale factor of 3 in the ydirection. For example when x = 6, (x  5)^{2} has a value of 1 but 3(x  5)^{2} has a value of 3, and when x has a value of 7, (x  5)^{2} has a value of 4 but 3(x  5)^{2} has a value of 12. Hence the two arms of the parabola are stretched upwards. y = 3 (x  5)^{2} Finally add 2 to the right side. This adds 2 to the yvalue of each point and has the effect of translating the curve 2 units upward, in the ydirection.
y = 3 (x  5)^{2} + 2 Now try this procedure with your expression,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 