Given the function:
Determine for which values of x the following holds:
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Given the function:
Determine for which values of x the following holds:
The function is quadratic with a negative leading coefficient, meaning the parabola opens downward. This implies that the function cannot be greater than zero for any real value of because it reaches its maximum (zero) at and decreases as increases.
Therefore, there are no values for which .
The correct choice reflecting this conclusion is: No x.
The graph of the function below does not intersect the \( x \)-axis.
The parabola's vertex is marked A.
Find all values of \( x \) where
\( f\left(x\right) > 0 \).
Since the leading coefficient is negative (-3/5), the parabola opens downward like an upside-down U. The highest point is at the vertex where , so it can never go above zero.
f(x) = 0 asks where the function equals zero (touches the x-axis). f(x) > 0 asks where the function is above the x-axis. For this downward parabola, it equals zero at x = 0 but is never above zero.
Look at the coefficient of ! If it's positive, the parabola opens upward (U-shape). If it's negative, it opens downward (upside-down U).
Absolutely! Graphing shows a downward parabola that touches the x-axis at (0,0) but never goes above it. This confirms there are no values where f(x) > 0.
Then the answer would be x = 0 only! The symbol ≥ means "greater than or equal to" so it includes the point where the function equals zero.
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