Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
-$$y = 3 x ^ { 2 } + 8 x - 16$$
A) $( - 4,0 )$
B) $( - 4,0 )$ and $\left( \frac { 4 } { 3 } , 0 \right)$
C) No x-intercepts
D) $( 4,0 )$ and $\left( - \frac { 4 } { 3 } , 0 \right)$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the quadratic function $y = 3x^2 + 8x - 16$, we set $y = 0$ and solve for $x$. This gives us a quadratic equation $3x^2 + 8x - 16 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 3$, $b = 8$, and $c = -16$, we find the roots of the equation. The calculation yields two real solutions, which correspond to the x-intercepts of the graph. Therefore, the correct answer is the one that lists two x-intercepts.

Use a Graphing Utility to Find or Approximate the X-Intercepts y=3x2+8x−16y = 3 x ^ { 2 } + 8 x - 16y=3x2+8x−16

Use a Graphing Utility to Find or Approximate the X-Intercepts $y = 3 x ^ { 2 } + 8 x - 16$