+128 The equation of a parabola is given.
y=1/4x^2−3x+18
What are the coordinates of the focus of the parabola?
+128460
y = (1/4)x^2 - 3x + 18 multiply through by 4
4y = x ^2 - 12x + 72 subtract 72 from both sides
4y - 72 = x^2 - 12x take (1/2) of 12 = 6, square it = 36 and add it to both sides
4y - 72 + 36 = x^2 - 12x + 36 factor the right side, simplify the right
4y - 36 = ( x - 6)^2 factor the left side as
4 ( y - 9) = ( x - 6)^2
And in the form
4p( y - k) = ( x - h)^2 the vertex is ( h, k) = (6, 9) and p = 1
So..... the focus is given by ( h, k + p) = ( 6, 9 + 1) = (6, 10 )
Here's the graph : https://www.desmos.com/calculator/eddman8tqs
