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2 years ago

Find the interval in which the function is positive.

Mathematics

1 answer:

blsea [12.9K]2 years ago

7 0

Answer:

(b) I, III

Step-by-step explanation:

The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).

<h3>General shape</h3>

The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.

If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.

<h3>Specific shape</h3>

The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).

f(2) = 2² -7·2 +10 = 4 -14 +10 = 0

f(5) = 5² -7·5 +10 = 25 -35 +10 = 0

This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.

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