so write f of x in the form blah blah blah okay so i can remember the name of the form this is like the parabolic form okay the normal form as you would say in german i think it is b squared plus c this is what we need to do for f of x being equal to two x squared plus four x plus nine okay i mean this is fairly easy because this is the same as two times x squared plus two x um so we need to complete the square what is still missing here is so we got a NUMBER_TOKEN here meaning we need to get yeah plus NUMBER_TOKEN and minus NUMBER_TOKEN. meaning what we have is two times x plus one squared then we get minus two plus nine is equal to two x plus one squared plus NUMBER_TOKEN. i think this should do the trick let me check NUMBER_TOKENx squared and we are going to get plus NUMBER_TOKENx then we are going to get plus NUMBER_TOKEN and yeah okay this right here is my answer for the first one that was easy um sketch the curve with the equation y is equal to f of x showing any points of intersection with the coordinates x's and coordinates of any turning point okay if i were to sketch this let me see so this one is shifted seven units in the upwards y direction this right here are seven units um so this is definitely what it's going to look like what we also have is a parabola which is going to be open in the upwards y direction meaning overall we are going to have no zeros
NO_SEGMENT_TOKEN