Find the domain of decrease of the function:
We have hundreds of course questions with personalized recommendations + Account 100% premium
Find the domain of decrease of the function:
To determine the domain over which the quadratic function is decreasing, we proceed by identifying the vertex of the parabola.
Given the form , we have , , and . The x-coordinate of the vertex can be found using the formula:
Substituting and into the formula, we calculate:
The vertex of the parabola occurs at . Since the function is a downward-opening parabola (as indicated by the negative coefficient of ), the function decreases for all values greater than the x-coordinate of the vertex.
Therefore, the domain of decrease for the function is .
This matches the answer choice:
Based on the data in the graph
Identify the domain where the function increases:
Look at the coefficient of ! If it's negative (like -1 in our function), the parabola opens downward. If it's positive, it opens upward.
Since our parabola opens downward, it reaches its highest point at the vertex (x = 1). After that peak, the function values get smaller as x increases, meaning it's decreasing.
The domain is all possible x-values (here: all real numbers). The domain of decrease is only the x-values where the function is getting smaller as x increases.
Pick test points! Choose values like x = 0, x = 1, and x = 2. Calculate for each. If y-values get smaller as x increases past the vertex, you've found the decreasing interval!
Yes! Every parabola has both increasing and decreasing intervals, separated by the vertex. The direction depends on whether the parabola opens upward or downward.
Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime