Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = x ^ { 2 } + 4 x + 10$$
A) No $x$-intercepts, $( 0,10 )$
B) No x-intercepts, $( 0 , - 10 )$
C) $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0 , - 10 )$
D) $\left( \frac { - 4 \pm \sqrt { 56 } } { 2 } , 0 \right)$,
$( 0,10 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts, we need to find where the function equals zero. Using the quadratic formula, we get:

$$x = \frac{-4 \pm \sqrt{4^2 - 4(1)(10)}}{2(1)} = -2 \pm\sqrt{6}i$$

Since these are complex numbers, there are no real x-intercepts. The y-intercept can be found by setting x=0:

$$y = 0^2 + 4(0) + 10 = 10$$

So the y-intercept is (0,10). Choice A correctly states that there are no x-intercepts and gives the y-intercept. Choices B, C, and D all contain incorrect information.

Find the X- and Y-Intercepts f(x)=x2+4x+10f ( x ) = x ^ { 2 } + 4 x + 10f(x)=x2+4x+10

Find the X- and Y-Intercepts $f ( x ) = x ^ { 2 } + 4 x + 10$