How to decompose fraction

Find the axis of symmetry of the graph of the function. (5 points) f(x) = 3x2 + 12x + 9

Kryger [21]

Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

<h3>Axis of symmetry</h3>

An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.

In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.

That is, in a quadratic function that has the form:

f(x)= ax² + bx + c

the axis of symmetry is a vertical line and it is defined as $x=\frac{-b}{2a}$ .

<h3>Axis of symmetry of f(x) = 3x² + 12x + 9</h3>

In this case, you know:

a= 3
b=12
c=9

Replacing in the definition of axis of symmetry:

$x=\frac{-12}{2x3}$

Solving:

$x=\frac{-12}{6}$

Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

Learn more about axis of symmetry:

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3 0

2 years ago

A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the poli

pishuonlain [190]

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

6 0

3 years ago

So llike a lil bit of help here?????

dimulka [17.4K]

Answer:

they saved the same amount of money each month

Step-by-step explanation:

5 0

3 years ago

Which is the slope of the graph of the equation below? X - y = 5

icang [17]

First, make it into slope intercept form. Subtract x form both sides

x (-x) - y = 5 (-x)

-y = -x + 5

Isolate the y. Divide -1 from both sides

(-y)/-1 = (-x + 5)/-1

y = x - 5

The slope in the form: y = mx + b, is m, which is next to the x

In this case, the m is 1

You're slope is 1

hope this helps

8 0

3 years ago

What is the association and are there any outliers?

kifflom [539]

Answer:

Hi there!

The correct answer is: There is a moderately strong, negative, nonlinear between two variables. There is one outlier around (3,40)

Step-by-step explanation:

The association in a scatter plot should always include a description of the <u>form</u>, <u>direction</u>, and <u>strength</u> of the association.

Form: Is the association linear or nonlinear?

Direction: Is the association positive or negative?

Strength: Does the association appear to be strong, moderately strong, or weak?

Outliers: Do there appear to be any data points that are unusually far away from the general pattern?

4 0

3 years ago