Y=-x^2-12x-37 find the 1) Roots 2) Factors 3) Vertex (x, y) 4) Interception with 'Y" axis 5) Axis of Symmetry 6)Direction of Opening 7)Max / Min ? Coordinates 8)Sketch 9) Domain 10) Range

1) The roots of the equation Y = -x² - 12·x - 37 are x = -6 - √73 and -6 + √73

2) The factors of the function Y = -x² - 12·x - 37 are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is (-6, -1)

4) The Y-intercept is (0, -37)

5) The axis of symmetry is x = -6

6) The parabola opens downward

7) The maximum point is (-6, -1)

8) The graph of the function created with Microsoft Excel is attached

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

Step-by-step explanation:

The given function is Y = -x² - 12·x - 37

1) The roots of the equation Y = -x² - 12·x - 37 is given as follows;

0 = -x² - 12·x - 37

∴ -x² - 12·x - 37 = 0

The roots are;

x = (12 ± √((-12)² - 4 × 1 × (-37)))/(-2)

∴ x = -6 - √73 and -6 + √73

2) The factors are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is given by h = -b/(2·a) = 12/(2) = -6

k = c - b²/(4·a) = -37 - 144/(-4) = -1

The vertex = (h, k) = (-6, -1)

4) The intercept with the "Y" axis is given when x = 0, therefore, the y-intercept is (0, -37)

5) The axis of symmetry can be found at the vertex or the line x = -6

6) The sign of the coefficient of x² is negative therefore, the parabola opens downward

7) The maximum point is given as follows;

At the maximum point, dY/dx = d(-x² - 12·x - 37)/dx = -2·x - 12 = 0

x = 12/(-2) = -6, which is the vertex, therefore Y = -(-6)² - 12×(-6) - 37 = -1

The maximum point is the vertex (-6, -1)

8) Please find attached the graph of the function created with Microsoft Excel

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.