Determine the x-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .
A) $( 0,0 ) , ( - 5,0 )$
B) $( - 7,0 ) , ( - 4,0 )$
C)no x-intercept(s)
D) $( - 7,0 ) , ( - 5,0 )$
E) $( - 2,0 ) , ( 2,0 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the quadratic function $f(x) = x^2 + 2x + 2$, we set $f(x) = 0$ and solve for $x$. This gives us the equation $x^2 + 2x + 2 = 0$. Using the discriminant $b^2 - 4ac$ from the quadratic formula, where $a = 1$, $b = 2$, and $c = 2$, we find that the discriminant is $2^2 - 4(1)(2) = 4 - 8 = -4$. Since the discriminant is negative, this means the quadratic equation has no real solutions and therefore the function has no x-intercepts.

Determine the X-Intercept(s) of the Quadratic Function f(x)=x2+2x+2f ( x ) = x ^ { 2 } + 2 x + 2f(x)=x2+2x+2

Determine the X-Intercept(s) of the Quadratic Function $f ( x ) = x ^ { 2 } + 2 x + 2$