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The correct statements regarding the behavior of a quadratic function are:
- The function in increasing for all real values of x where -6 < x < -2.
- The function is decreasing for all real values of x where x < -6 or x > -2.
A quadratic function with roots and
is defined by:
In which a is the leading coefficient.
The coefficient influences the behavior, as follows:
- If a < 0, the function is increasing between the roots, and decreasing otherwise.
- If a > 0, the function is decreasing between the roots, and increasing otherwise.
In this problem, the function is:
f(x) = -(x + 6)(x + 2).
The roots are x = -6 and x = -2, and the leading coefficient is of a = -1 < 0, hence:
- The function in increasing for all real values of x where -6 < x < -2.
- The function is decreasing for all real values of x where x < -6 or x > -2.
More can be learned about quadratic functions at brainly.com/question/24737967
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Answer:
x = ± 2
Step-by-step explanation:
Given
x² + 5 = 3x² - 3 ( subtract x² + 5 from both sides )
0 = 2x² - 8 ( add 8 to both sides )
8 = 2x² ( divide both sides by 2 )
4 = x² ( take the square root of both sides )
x = ± = ± 2