take square root of both sides of the equation to get y = plus or minus sqrt(-x + 9).
the y-intercept is the value of y when x = 0.
equation becomes y = plus or minus sqrt(9) = plus or minus 3.
the x-interceptis the value of x when y = 0
start with y = plus or minus sqrt(-x + 9).
set y = 0 to get 0 = plus or minus sqrt(-x + 9)
this breaks up into two equaitons.
0 = sqrt (-x + 9)
0 = - sqrt (-x + 9)
square both sides of each equation to get:
0 = -x + 9
0 = -(-x + 9)
solve for x in each equation to get:
x = 9
x = 9
the x-intercept is x = 9.
the y-intercept is y = plus or minus 3.
if the graph is symmetric about the y-axis, then f(x) = f(-x).
the equation is y^2 = -x + 9.
after solving for y, we get y = plus or minus sqrt(-x + 9)
we let y = f(x) to get:
f(x) = plus or minus sqrt(-x + 9)
f(-x) = plus or minus sqrt(x + 9)
if the equation was symmetric about the y-axis, then f(x) would be equal to f(-x) which it is clearly not.
if the graph is symmetric about the x-=axis, then f(x) = -f(x).
our equation is y^2 = -x + 9.
after solving for y, we get y = plus or minus sqrt(-x + 9)
we let y = f(x) to get:
f(x) = plus or minus sqrt(-x + 9)
-f(x) = minus (plus or minus sqrt(-x + 9)
if they are equal, then plus or minus sqrt(-x + 9) = minus (plus or minus sqrt(-x + 9)
a minus times a plus is equal to a minus.
a minus times a minus is equal to a plus.
therefore minus (plus or minus sqrt(-x + 9) becomes:
minus or plus sqrt(-x + 9), which is the same as:
plus or minus sqrt(-x + 9).
therefore f(x) = -f(x) and the equation is symmetric about the x-axis.
here's what the graph looks like:
