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) 24
B) $\frac { 3 } { 2 }$
C) 9
D) $- 9$

Question

Quizplus · Accepted Answer

A quadratic function has exactly one $x$-intercept when its discriminant ($b^2 - 4ac$) is equal to 0. For the given function $f(x) = x^2 - 6x + c$, $a = 1$, $b = -6$, and $c$ is the unknown. Plugging into the discriminant formula gives $(-6)^2 - 4(1)(c) = 0$. Simplifying, $36 - 4c = 0$, which leads to $c = 9$.

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 $f ( x ) = x ^ { 2 } - 6 x + c$