Answer:
Step-by-step explanation:
Please, share the answer options next time.
1) f(x) = 2x^2– x – 6 is a quadratic function.
2) The coefficients of this polynomial are a = 2, b = -1 and c = -6
2) Its graph opens up.
3) The x-value of the axis of symmetry and the vertex is x = -b / (2a), which here comes out to x = -(-1) / [2(2)], or x = 1/4
4) the y coordinate of the vertex is f(1/4), or -6 1/8
5) The vertex is at (1/4, -6 1/8)
6) The y-intercept is at f(0): 2(0)^2 - 0 - 6 = -6 => (0, -6)
Answer:
Step-by-step explanation:
x² + b²/4a² = -c / a + b²/4a²
x² + (b/2a)² = -c/a + (b/2a)²
(x + b/2a)² = -c/a + (b/2a)² = -c / a + b²/4a² = (-4ac+ b²)/4a²
(x + b/2a)² = (-4ac+ b²)/4a²
√{(x + b/2a)²} = √{(-4ac+ b²)/4a²}
x + b/2a = √(-4ac+ b²) / √(4a²) = √(-4ac+ b²) / 2a = √( b²-4ac) / 2a
x + b/2a = √( b²-4ac) / 2a
- subtract b/2a from both sides
x + b/2a -b/2a = {√( b²-4ac) / 2a } -b/2a
x = -b/2a + {√( b²-4ac) / 2a }
x = {-b±√( b²-4ac)}/2a
Answer: B) 4
Step-by-step explanation:
Using the formula
Standard deviation = √( (Σ ( x - π)²)/n)
To get the standard deviation, first we workout the Mean which is the simple average of the data set
n = 4
(13 + 17 + 9 + 21) / 4 = 60/4 = 15
Mean(x) = 15
Then (x-π)²
13 - 15 = (-2)² = 4
17 - 15 = (2)² = 4
9 - 15 = (-6)² = 36
21 - 15 = (6)² = 36
Σ ( x - π)² = (4 + 4 + 36 + 36) = 80
Standard deviation = √( (Σ ( x - π)²)/n
= √ (80/4)
=√20
= 4.47
= 4
Given that a is an integer from -22 to 0 such that a is equivalent to 43 (mod 23).
Such a can be obtained as follows:
a = 43 (mod 23) - 23 = 20 - 23 = -3.
Therefore, a = -3.
