Find the x- and y-intercepts: $$f ( x ) = 4 x ^ { 2 } - 6 x + 9$$
A) $\left( \frac { - 4 + \sqrt { 13 } } { 7 } , 0 \right) , \left( \frac { - 4 - \sqrt { 13 } } { 7 } , 0 \right) ; ( 0,9 )$
B) No x-intercepts; (0, 9)
C) $\left( \frac { 4 + \sqrt { 13 } } { 7 } , 0 \right) , \left( \frac { 4 - \sqrt { 13 } } { 7 } , 0 \right) ; ( 0 , - 9 )$
D) $\left( \frac { 4 + \sqrt { 13 } } { 14 } , 0 \right) , \left( \frac { 4 - \sqrt { 13 } } { 14 } , 0 \right) ; ( 0,9 )$
E) $( 4 + \sqrt { 13 } , 0 ) , ( 4 - \sqrt { 13 } , 0 ) ; ( 0,9 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts, we set $f(x) = 0$ and solve for $x$. However, the discriminant of the quadratic equation $4x^2 - 6x + 9 = 0$ is $b^2 - 4ac = (-6)^2 - 4(4)(9) = 36 - 144 = -108$, which is negative, indicating there are no real solutions and hence no x-intercepts. The y-intercept is found by setting $x = 0$, which gives $f(0) = 4(0)^2 - 6(0) + 9 = 9$, so the y-intercept is $(0, 9)$.

Find the X- and Y-Intercepts f(x)=4x2−6x+9f ( x ) = 4 x ^ { 2 } - 6 x + 9f(x)=4x2−6x+9

Find the X- and Y-Intercepts $f ( x ) = 4 x ^ { 2 } - 6 x + 9$