The graph of the function below does not intersect the -axis.
The parabola's vertex is marked A.
Find all values of where
.
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The graph of the function below does not intersect the -axis.
The parabola's vertex is marked A.
Find all values of where
.
To solve this problem, we need to determine the range of values where the quadratic function is negative.
Given that the graph of the function does not intersect the -axis, it suggests that all real-valued outputs of the function have the same sign. This occurs because there are no real roots (solutions) to the equation .
We identify that the quadratic function's parabola is opening upwards (concave up) because it does not intersect the -axis, typically implying the entire parabola is either fully below or fully above the axis, without cutting through it.
If the parabola were above the axis, at the vertex (marked A), the function's value would be positive, and all corresponding function values would also be positive along the width of the parabola. Conversely, if it were below the axis and since the graph maintains this position, the entire function would remain negative.
The problem indicates that the parabola does not intersect or touch the -axis, highlighting that does not reach zero but maintains positivity or negativity uniformly along the span of .
Since the final answer choice deduces that does not enter a negative domain by naturally coasting along the positive regional track, the suitable conclusion is that the function has no negative domain, so there are no such values.
No such values.
The graph of the function below intersects the X-axis at points A and B.
The vertex of the parabola is marked at point C.
Find all values of \( x \) where \( f\left(x\right) > 0 \).
Look at where the parabola sits! If it opens upward and stays above the x-axis (like this one), all y-values are positive. If it stayed below the x-axis, all y-values would be negative.
It means the equation has no real solutions. The parabola never touches or crosses the x-axis, so it's either entirely above or entirely below it.
Because the entire parabola is positive! Since vertex A is above the x-axis and the parabola opens upward, for all values of x. There are no x-values where .
From the graph, we can see it opens upward (U-shaped). If it opened downward and didn't intersect the x-axis, then it would be entirely below the axis, making all values negative.
Look at the shape! If it's U-shaped (like a smile), it opens upward. If it's ∩-shaped (like a frown), it opens downward. The vertex is either the lowest point (upward) or highest point (downward).
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