Question

tell whether the graph opens upward or downward. then find the axis of symmetry and vertex of the graph of the function

1. y=xsquared-5
2. y=-2*xsquared+6x+7

Answer 1

x^2 = (y + 5)
when x gets big, y gets big, opens up (holds water)
symmetric about y axis (x = 0)
vertex at (0,-5)

2 x^2 - 6 x = - y + 7

x^2 - 3 x = -(1/2)y + 7/2

add (3/2)^2 = 9/4 to both sides
x^2 -3 x +9/4 = -(2/4)y + 23/4
(x-3/2)^2 = -(1/4)(2y-23)
axis at x = 3/2
vertex at (3/2 , 23/2)
when x gets big, y gets big negative. Opens down (sheds water)