Determine the x- and y-intercepts for the given function.
-$$f ( x ) = - ( x - 2 ) ^ { 2 } - 4$$
A) $x$-intercepts: $( 0,0 )$ and $( 4,0 )$
$y$-intercept: $( 0 , - 8 )$

B) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0 , - 4 )$

C) $x$-intercept: none
$y$-intercept: $( 0 , - 8 )$

D) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0,4 )$

Question

Determine the x- and y-intercepts for the given function.
-$$f ( x ) = - ( x - 2 ) ^ { 2 } - 4$$
A) $x$-intercepts: $( 0,0 )$ and $( 4,0 )$
$y$-intercept: $( 0 , - 8 )$

B) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0 , - 4 )$

C) $x$-intercept: none
$y$-intercept: $( 0 , - 8 )$

D) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0,4 )$

Quizplus · Accepted Answer

The function is a downward-opening parabola with vertex at (2, -4). It does not cross the x-axis, so there are no x-intercepts. The y-intercept is found by setting x = 0, giving y = -8.

Determine the X- and Y-Intercepts for the Given Function f(x)=−(x−2)2−4f ( x ) = - ( x - 2 ) ^ { 2 } - 4f(x)=−(x−2)2−4

Determine the X- and Y-Intercepts for the Given Function $f ( x ) = - ( x - 2 ) ^ { 2 } - 4$