over which interval is the graph of f(x)=-x² + 3x + 8 increasing? (-∞, 1.5) (-∞, 10.25) (1.5, ∞) (10.25, ∞)
over which interval is the graph of f(x)=-x² + 3x + 8 increasing? (-∞, 1.5) (-∞, 10.25) (1.5, ∞) (10.25, ∞)
Answer
Explanation:
Step1: Recall the formula for the vertex - x - coordinate
For a quadratic function (y = ax^{2}+bx + c), the x - coordinate of the vertex is (x=-\frac{b}{2a}). In (f(x)=-x^{2}+3x + 8), (a=-1) and (b = 3). [x=-\frac{3}{2\times(-1)} = 1.5]
Step2: Determine the increasing interval
Since (a=-1<0), the parabola opens downwards. The function is increasing to the left of the vertex. So the increasing interval is ((-\infty,1.5)).
Answer:
((-\infty,1.5))