The function given by $f ( x ) = - 16 x ^ { 2 } - 7$ has no x-intercepts.

Question

Quizplus · Accepted Answer

An x-intercept occurs where the graph of the function crosses the x-axis, which means the function value (y-value) is 0. For the given quadratic function $f(x) = -16x^2 - 7$, setting it equal to 0 gives $-16x^2 - 7 = 0$. Solving for x would involve taking the square root of a negative number (since there's no x value that can make $-16x^2$ equal to 7), which is not possible in the set of real numbers. Therefore, the function has no real x-intercepts.

The Function Given By f(x)=−16x2−7f ( x ) = - 16 x ^ { 2 } - 7f(x)=−16x2−7

The Function Given By $f ( x ) = - 16 x ^ { 2 } - 7$