# Determine the vertex and the axis of symmetry for the function below y=x^2+4x+1

vertex; (-2, -3)

axis of symmetry; x = -2

hope this helps, God bless!

the squared variable is the "x", thus is a vertical parabola, thus, the axis of symmetry will occur over the x-coordinate of the vertex, and thus will be

Axis of Symmetry: x = 3

Vertex: (3, 5)

Step-by-step explanation:

Use a graphing calc.

f(x)=(x−3)2−5

Find the properties of the given parabola.

Direction:

Vertex: (3,−5)

Focus: (3,−194)

Axis of Symmetry: x=3

Directrix: y=−214

Select a few x

values, and plug them into the equation to find the corresponding y values. The x

values should be selected around the vertex.

x y

1 -1

2 -4

3 -5

4 -4

5 -1

Graph the parabola using its properties and the selected points.

Direction:

Vertex: (3,−5)

Focus: (3,−194)

Axis of Symmetry: x=3

Directrix: y=−214

x y

1 -1

2 -4

3 -5

4 -4

5 -1

See attached image

Step-by-step explanation:

This equation for a parabola is given in vertex form, so it is very simple to extract the coordinates of its vertex, by using the opposite of the number that accompanies the variable "x" in the squared expression (opposite of 2) for the vertex's x-value, and the value of the constant (-6) for the vertex's y-value.

The vertex coordinates are therefore: (-2,-6)

The equation of the axis of symmetry of the parabola is a vertical line passing through the vertex. Since all vertical lines have the shape x = constant in our case, in order to pass through (-2,-6) the vertical line is defined by the equation: x = -2.

See image attached to find the vertex drawn as a red point, and the axis of symmetry as an orange vertical line passing through it.

See below in bold.

Step-by-step explanation:

This is the vertex form of a parabola which opens upwards.

To find the x intercept put h(x) = 0:

(x + 1)^2 - 4 = 0

(x + 1)^2 = 4

x + 1 = +/- 2

x = (-3, 0) an (1, 0) are the x-intercepts.

For the y-intercept we put x = 0

y = (0+1)^2 - 4 = -3

y-intercept = (0, -3).

The vertex is (-1, -4).

Axis of symmetry is x = -1.

Read more on -

The vertex is located at (3,5)

The axis of symmetry is x = 3

The plot is in the image attached

Step-by-step explanation:

First we need to find the vertex of the quadratic function. We can find the x-coordinate of the vertex using the formula:

x_v = -b / 2a

Where 'a' and 'b' are coefficients of the quadratic equation in the model:

ax^2 + bx + c = 0

Then we need to expand the terms of f(x):

f(x) = (x-3)^2 + 5

f(x) = x^2 - 6x + 9 + 5

f(x) = x^2 - 6x + 14

So we have a = 1 and b = -6

Then the x-coordinate of the vertex is:

x_v = 6 / 2 = 3

We can use this value in f(x) to find the y-coordinate of the vertex:

f(x_v) = 3^2 - 6*3 + 14 = 5

So the vertex is located at (3,5)

The axis of symmetry is the vertical line traced in the vertex, so it is x = 3

The plot is in the image attached. The circle at (3,5) is the vertex, and the blue line is the axis of symmetry.