A parabola has been drawn on a graph but there is information missing. The equation has not been written on the curve. It has a minimum turning point, a y intercept of +6 and cuts the x-axis at +2 and +#
Determine the equation to the curve
2 answers
x-axis at +2 and +3
axis of symmetry is halfway between 2 and 3 or x =2.5
to get the zeros of y at x = 2 and 3
y = k (x-2)(x-3)
to get y = 6 at x = 0
6 = k (-2)(-3)
k = 1
so
y = x^2 -5 x + 6 (answer)
check if vertex is at x = 2.5 by completing the square
y -6 = x^2 - 5 x
y - 6 + (5/2)^2 = x^2 - 5 x + (5/2)^2
y + .25 = (x-2.5)^2
so vertex at (2.5 , -.25) checks :)
to get the zeros of y at x = 2 and 3
y = k (x-2)(x-3)
to get y = 6 at x = 0
6 = k (-2)(-3)
k = 1
so
y = x^2 -5 x + 6 (answer)
check if vertex is at x = 2.5 by completing the square
y -6 = x^2 - 5 x
y - 6 + (5/2)^2 = x^2 - 5 x + (5/2)^2
y + .25 = (x-2.5)^2
so vertex at (2.5 , -.25) checks :)
1 answer