Find the turning point of the line y = -2x^2 +5x -9

The first step in finding any turning point is to differentiate. To do this, we muiltiply x by its power and drop the power by 1. so in this senario we multiply the -2x by 2 giving us -4x and the power becomes 1, we then multiply the 5x by 1 and the power becomes 0, x^0=1 so we can simply write 5. lastly we can disregard the constant as it has no x value. So we then have the equation, Dy/dx= -4x +5. At a turning point, the gradiant = 0, which means we can set the differentiated equation equal to 0 to find the x-value of the turning point. 0= -4x + 5, if we -5 from both sides we have -5= -4x, then devide both sides by -4 to give you x= -5/-4, this is the x value of the turning point. The last step is to plug the x value into the original value to find the y-value of the turning point y = -2(-5/-4)^2 + 5(-5/-4) - 9, if you put this into your calculator you get the y-value = -47/8. so the turning point has co-ordinates (-5/-4, -47/8)