Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$-intercept?
A) $\frac { 16 } { 3 }$
B) $- \frac { 2 } { 3 }$
C) 16
D) $\frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

For a quadratic function to have exactly one $x$-intercept, its discriminant ($b^2 - 4ac$) must equal 0. Here, $a = 3$, $b = 8$, and $c$ is unknown. The discriminant is $8^2 - 4(3)c = 64 - 12c$. Setting this equal to 0 gives $64 - 12c = 0$, solving for $c$ gives $c = \frac{64}{12} = \frac{16}{3}$.

Provide an Appropriate Response ccc Does the Quadratic Function f(x)=3x2+8x+cf ( x ) = 3 x ^ { 2 } + 8 x + cf(x)=3x2+8x+c

Provide an Appropriate Response $c$ Does the Quadratic Function $f ( x ) = 3 x ^ { 2 } + 8 x + c$