how do you graph y=25-x^2?

Question

how do you graph y=25-x^2

you don't have to actually graph it, but explain what the steps are and what you have to do.

Answer 1

f (x) = 25 - x²
f `(x) = - 2x
f " (x) = - 2

For turning point , f `(x) = 0
- 2x = 0
x = 0
f " (x) is - ve
(0 , 25) is a MAXIMUM turning point.
Cuts x axis at 25 - x² = 0
x ² = 25
x = ± 5
Points on curve are then:-
(0, 25) , (5 , 0) , (- 5 , 0)

Answer 2

it's y=-x^2+25
y=(-x+5)(x+5)


x intercept is both 5 and -5
y intercept is 25

Answer 3

parabola opens down (because x^2 is negative)
crosses y axis where x=0, so (0,25)
crosses x axis where y=0, so (5, 0) and (-5, 0)