Maths-

General

Easy

Question

# Find the axis of symmetry, vertex and y-intercept of the function

f(x) = -x^{2} - 2x – 5

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: 0

### 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 – 5, a= -1, b= -2, and c= -5. 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 – 5 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) - 5

k = -(-1)^{2} - 2(-1) - 5

k = -1 + 2 - 5

k = -4

Therefore, the vertex is (-1 , -4)

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

y = -(0)^{2} - 2(0) - 5

y = 0 - 0 - 5

y = -5

Therefore, Axis of symmetry is x = -1

Vertex is ( -1 , -4)

Y- intercept is -5.

The equation of the axis of symmetry for f(x)= -x

^{2}- 2x – 5 is x = -1.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}- 2(h) - 5

^{2}- 2(-1) - 5

Therefore, the vertex is (-1 , -4)

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

^{2}- 2(0) - 5

Therefore, Axis of symmetry is x = -1

Vertex is ( -1 , -4)

Y- intercept is -5.

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