Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Question

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$-intercepts? A) $a < 9$ B) $a < 3$ C) $a > 9$ D) $a > 3$

Quizplus · Accepted Answer

For a quadratic function to have no $x$-intercepts, the discriminant ($b^2 - 4ac$) must be less than 0. For $f(x) = ax^2 - 6x + 3$, the discriminant is $(-6)^2 - 4(a)(3) = 36 - 12a$. Setting this less than 0 gives $36 - 12a < 0$, which simplifies to $a > 3$.

Provide an Appropriate Response f(x)=ax2−6x+3f ( x ) = a x ^ { 2 } - 6 x + 3f(x)=ax2−6x+3

Provide an Appropriate Response $f ( x ) = a x ^ { 2 } - 6 x + 3$