1.) What is the vertex of the quadratic function y=x^2-4x-1

Mathematics

1 answer:

Serjik [45]3 years ago

4 0

1. Solve by differentiation (Derivative = 0 at the vertex)

dy/dx= 2x-4

0=2x-4

0=2(x-2)

x=2

when x=2 y=-5

therefore vertex (2,-5)

You might be interested in

Given that ∠Ф = 180°, determine the numerical value of this function.

Rudiy27

Answer:

The answer to your question is 3. 0

Step-by-step explanation:

For an angle of 180°:

- hypotenuse = 1

- Adjacent side = 1

- Opposite side = 0

Then, sin Ф = $\frac{Opposite side}{Hypotenuse}$

sin 180° = $\frac{0}{1}$

sin 180° = 0

8 0

2 years ago

The position s(t) of a robot moving along a track at time t is given by s(t)=9t^2−90t+4.

Xelga [282]

The total distance traveled by the robot from t=0 to t=9 is 1422 units

Integration is a way in which smaller components are brought together in pieces to form a whole. Integration can be used in finding areas, volumes and so on.

Given that the position s(t) at any time t is given by the function:

s(t)=9t²−90t+4

The total distance traveled by the robot from t=0 to t=9 can be gotten by integrating the position function within the limits 0< t < 9

Therefore:

$Total\ distance = \int\limits^9_0 {s(t) \, dt \\\\Total\ distance = \int\limits^9_0 {(9t^2-90t+4) \, dt\\\\Total\ distance = [3t^3-45t+4t]_0^9\\\\Total\ distance=-1422\ units$