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goldfiish [28.3K]
3 years ago
11

For the function F(x) = 2x^2-31x-51, where is the function increasing and positive? ( for all X values greater than what number

)
Mathematics
1 answer:
Ulleksa [173]3 years ago
7 0
ANSWER
x \: > \: 17

EXPLANATION

The given function is

f(x) = 2 {x}^{2} - 31x - 51
Let us split the middle term to get,

f(x) = 2 {x}^{2} -34x + 3x- 51

We factor to obtain,

f(x) = 2x(x - 17) -+3(x - 17)

f(x) = (2x -+3)(x -17)

Let us find the zeros of f(x),

(2x +3)(x - 17) = 0

Either

2x +3 = 0 \: or \: x - 17 = 0
x = -\frac{3}{2} \: or \: x = 17

We need to find the x-value of the vertex, which is the midpoint of the x-intercepts.

This gives us,

\frac{- \frac{3}{2} + 17}{2} = 7.75
Hence the axis of symmetry of the parabola has equation,

x = 7.75

Since the given function has minimum turning point, it will decrease and then increase.

The function will be increasing for
x \: > \: 7.75

The function will be increasing and positive for
x \: > \: 17
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Using a z-table (http://www.z-table.com) we see that the z-score associated with an area to the left of 0.05 is between -1.64 and -1.65; since it is equally distant from both we will use -1.645.

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