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) $- \frac { 2 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 16 } { 3 }$
D) 16

Question

Quizplus · Accepted Answer

A quadratic function has exactly one $x$-intercept when its discriminant ($b^2 - 4ac$) equals 0. For $f(x) = 3x^2 + 8x + c$, 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 $f ( x ) = 3 x ^ { 2 } + 8 x + c$