Maths-

General

Easy

Question

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

f(x) = 0.4x^{2} + 1.6x

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)= 0.4x^{2} + 1.6x, a= 0.4, b= 1.6, and c= 0. So, the equation for the axis of symmetry is given by

x = −(1.6)/2(0.4)

x = -1.6/0.8

x = -2

The equation of the axis of symmetry for f(x)= 0.4x^{2} + 1.6x is x = -2.

The x coordinate of the vertex is the same:

h = -2

The y coordinate of the vertex is :

k = f(h)

k = 0.4(h)^{2} + 1.6h

k = 0.4(-2)^{2} + 1.6(-2)

k = 1.6 – 3.2

k = -1.6

Therefore, the vertex is (-2 , -1.6)

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

y = 0.4(0)^{2} + 1.6(0)

y = 0 + 0

y = 0

Therefore, Axis of symmetry is x = -2

Vertex is ( -2 , -1.6)

Y- intercept is 0.

The equation of the axis of symmetry for f(x)= 0.4x

^{2}+ 1.6x is x = -2.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ 1.6h

^{2}+ 1.6(-2)

Therefore, the vertex is (-2 , -1.6)

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

^{2}+ 1.6(0)

Therefore, Axis of symmetry is x = -2

Vertex is ( -2 , -1.6)

Y- intercept is 0.

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