You have the following function:
f(x) = x² - 4x - 21
in order to determine the vertex and y-intercept of the function, proceed as follow:
For the y-intercept, replace x=0 into the given function:
f(0) = 0² - 4(0) - 21
f(0) = -21
the y-intercept is -21
for the vertex, cosnider that the x coordinate of the vertex is given by:
x = -b/2a
where a and b are coefficients of the polynomial ax² + bx + c. In this case, you have:
a = 1
b = -4
then, the x coordinate of the vertex is:
x = -(-4)/2(1)
x = 2
and the y-intercept is the value of f(x) at the vertex, that is, f(2):
f(2) = 2² - 4(2) - 21
f(2) = 4 - 8 - 21
f(2) = -25
Hence, the vertex of the function is (2,-25)
