Find the domain of increase of the function:
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Find the domain of increase of the function:
To find the domain of increase for the function , let's determine the vertex first.
Plug in the values for and :
The x-coordinate of the vertex is .
Since the coefficient is negative, this means the parabola opens downwards. A parabola opening downward will increase until it reaches the vertex, then start decreasing.
Therefore, the domain on which the function is increasing is .
Therefore, the solution to the problem is .
Note that the graph of the function shown below does not intersect the x-axis
The parabola's vertex is A
Identify the interval where the function is decreasing:
Look at the coefficient of ! If it's positive, the parabola opens upward (U-shape). If it's negative like our -1, it opens downward (∩-shape).
Domain is where the function exists (all real numbers for quadratics). Domain of increase is the specific interval where y-values get larger as x increases.
Because x = 1 is the vertex (highest point) of this downward-opening parabola. The function climbs up to this peak, then falls down afterward.
Yes! The vertex formula is the most reliable way to find where a quadratic function changes from increasing to decreasing (or vice versa).
If a > 0, the parabola opens upward. Then the function would decrease until the vertex and increase after the vertex - the opposite of our current problem!
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