Put the equation below into vertex form.

y=(x+9)(x+25)

Step-by-step explanation:

1) The equation is given in factored form

2) The key characteristics of the parabola are;

a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are (1/2, 0) and (-6, 0)

c. The y intercept is (0, -6)

d. The vertex point is (-2.75, -21.125)

Step-by-step explanation:

The given equation is f(x) = (2·x -1)(x + 6)

Therefore the equation is given in factored form

The key characteristic of the parabola revealed from the form f(x) = (2·x -1)(x + 6) are;

1) Writing the parabola in the intercept form, a(x - p)(x -q) we have;

f(x) = (2·x -1)(x + 6) = 2·(x - 1/2)(x + 6)

p = 1/2, q = -6

Therefore;

Given that a is positive the parabola is concave upwards

2) a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are p and q which are (1/2, 0) and (-6, 0)

c. The y intercept is a·(-p)·(-q) = 2×(-1/2)×6 = -6

The y intercept is (0, -6)

d. Expanding we get;

f(x) = 2·x² + 11·x - 6

From the

The vertex is h = -b/(2·a) = -11/(2×2) = -2.75

h(2.75) = 2×(-2.75)² + 11×(-2.75) - 6 = -21.125

Therefore, the function is symmetrical about the vertex point (-2.75, -21.125)

1) The equation is given in factored form

2) The key characteristics of the parabola are;

a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are (1/2, 0) and (-6, 0)

c. The y intercept is (0, -6)

d. The vertex point is (-2.75, -21.125)

Step-by-step explanation:

The given equation is f(x) = (2·x -1)(x + 6)

Therefore the equation is given in factored form

The key characteristic of the parabola revealed from the form f(x) = (2·x -1)(x + 6) are;

1) Writing the parabola in the intercept form, a(x - p)(x -q) we have;

f(x) = (2·x -1)(x + 6) = 2·(x - 1/2)(x + 6)

p = 1/2, q = -6

Therefore;

Given that a is positive the parabola is concave upwards

2) a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are p and q which are (1/2, 0) and (-6, 0)

c. The y intercept is a·(-p)·(-q) = 2×(-1/2)×6 = -6

The y intercept is (0, -6)

d. Expanding we get;

f(x) = 2·x² + 11·x - 6

From the

The vertex is h = -b/(2·a) = -11/(2×2) = -2.75

h(2.75) = 2×(-2.75)² + 11×(-2.75) - 6 = -21.125

Therefore, the function is symmetrical about the vertex point (-2.75, -21.125)

The answer is in the image 

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

The answer is in the image 

The answer is in the image 

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km