Maths-

General

Easy

Question

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

f(x) = x^{2} - 6x + 12

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: 12

### 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} - 6x + 12, a= 1, b= -6, and c= 12. So, the equation for the axis of symmetry is given by

x = −(-6)/2(1)

x = 6/2

x = 3

The equation of the axis of symmetry for f(x)= x^{2} - 6x + 12 is x = 3.

The x coordinate of the vertex is the same:

h = 3

The y coordinate of the vertex is :

k = f(h)

k = h^{2} – 6h + 12

k = (3)^{2} - 6(3) + 12

k = 9 – 18 + 12

k = 3

Therefore, the vertex is (3 , 3)

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

y = (0)^{2} - 6(0) + 12

y = 0 + 0 + 12

y = 12

Therefore, Axis of symmetry is x = 3

Vertex is (3 , 3)

Y- intercept is 12.

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

^{2}- 6x + 12 is x = 3.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}– 6h + 12

^{2}- 6(3) + 12

Therefore, the vertex is (3 , 3)

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

^{2}- 6(0) + 12

Therefore, Axis of symmetry is x = 3

Vertex is (3 , 3)

Y- intercept is 12.

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