Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$-intercept?
A) $\frac { 3 } { 2 }$
B) 9
C) 24
D) $- 9$

Question

Quizplus · Accepted Answer

For a quadratic function to have exactly one $x$-intercept, the discriminant ($b^2 - 4ac$) must equal 0. Here, $a = 1$, $b = -6$, and $c$ is unknown. The discriminant is $(-6)^2 - 4(1)(c) = 36 - 4c$. Setting this equal to 0 gives $36 - 4c = 0$, solving for $c$ gives $c = 9$.

Provide an Appropriate Response ccc Does the Quadratic Function f(x)=x2−6x+cf ( x ) = x ^ { 2 } - 6 x + cf(x)=x2−6x+c

Provide an Appropriate Response $c$ Does the Quadratic Function $f ( x ) = x ^ { 2 } - 6 x + c$