Maths-

General

Easy

Question

# Graph f(x) = x^{2} + 2x + 4. What are axis of symmetry, vertex and y-intercept of the function

Hint:

### For a quadratic function is in standard form, f(x)=ax2+bx+c.

A vertical line passing through the vertex is called the axis of symmetry for the parabola.

Axis of symmetry x=−b/2a

Vertex The vertex of the parabola is located at a pair of coordinates which we will call (*h, k*). where h is value of x in axis of symmetry formula and k is f(h).

The *y*-intercept is the point where a graph crosses the *y*-axis. In other words, it is the value of *y* when x=0.

## The correct answer is: 4

** **

This quadratic function is in standard form, f(x)=ax^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In f(x)=x^{2}+2x+4, a=1, b=2, and c=4. So, the equation for the axis of symmetry is given by

X = −(2)/2(1)

x = - 2/2

x = -1

The equation of the axis of symmetry for f(x)=x^{2}+2x+4 is x = -1.

The x coordinate of the vertex is the same:

h = -1

The y coordinate of the vertex is :

k = f(h)

k = (h)^{2} + 2(h) + 4

k = (-1)^{2} + 2(-1) + 4

k = 1 – 2 + 4

k = 3

Therefore, the vertex is (-1 , 3)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = (0)^{2} + 2(0) + 4

y = 0 + 0 + 4

y = 4

Therefore, Axis of symmetry is x = -1

Vertex is ( -1 , 3 )

Y- intercept is 4.

This quadratic function is in standard form, f(x)=ax

^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In f(x)=x

^{2}+2x+4, a=1, b=2, and c=4. So, the equation for the axis of symmetry is given by

X = −(2)/2(1)

x = - 2/2

x = -1

The equation of the axis of symmetry for f(x)=x^{2}+2x+4 is x = -1.

The x coordinate of the vertex is the same:

h = -1

The y coordinate of the vertex is :

k = f(h)

k = (h)^{2} + 2(h) + 4

k = (-1)^{2} + 2(-1) + 4

k = 1 – 2 + 4

k = 3

Therefore, the vertex is (-1 , 3)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = (0)^{2} + 2(0) + 4

y = 0 + 0 + 4

y = 4

Therefore, Axis of symmetry is x = -1

Vertex is ( -1 , 3 )

Y- intercept is 4.

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