Question

Find the point on the parabola y = x^2 -5x + 6 that's closest to the origin.

Answer 1

the general co ordinate of a point on the graph is

(x, x^2 -5x +6) { x,y}

Answer 2

the distance of this point o the origin is

sqrt( x^2 + (x^2 -5x+6)^2 )

Answer 3

so d= sqrt{ x^2 +(x^2 -5x+6)^2}

Answer 4

but , minimising the sqrt is the same as minimising the expression under the sqrt

Answer 5

so take d=distance = x^2 +(x^2 -5x+6)^2

and minimise that function

Answer 6

the minimum will occur when x= 3/2

Answer 7

then sub this value back into the function to get the y ordinate