How do you graph y= 6x^2 and show the vertex, axis of symmetry, and x-intercepts of the equation?

1 Answer
Dec 9, 2017

Graph of y = 6x^2 is available as part of this solution.

Vertex = (0,0)

Axis of Symmetry is the line x = 0

x-intercept x =(0,0)

Explanation:

We are given the quadratic equation y = 6x^2 color(red)(..Equation.1)

Graph of the Quadratic Equation y = 6x^2 is below:

enter image source here

Let us investigate the graph:

How do we find the X Intercept?

To find the x-intercept of the equation we let y = 0 and then solve for x.

Using Point Notation it is written as (x, 0)

How do we find the Y Intercept?

To find the y-intercept of the equation we let x = 0 and then solve for y.

Using Point Notation it is written as (0, y)

How do we find the Axis of Symmetry?

x-coordinate of the Vertex is the Equation of the Axis of Symmetry of the Parabola.

color(green)(Step.1)

How do we find the Vertex of a Parabola?

Standard Form of a Quadratic Equation is

** y = f(x) = ax^2+bx+c

The expression -b/(2a) will give us the x-coordinate of the Vertex.

Hence, we get -(0)/2*(6) = 0

We can obtain the y-coordinate of y = 6x^2 by substituting the value of x = 0

Hence, 0 = 6(0)^2

rArr y = 0

Hence, our Vertex = (0,0)

color(green)(Step.2)

x-intercept is obtained by:

Let y = 0 in color(red)(..Equation.1)

rArr 0 = 6x^2

rArr x^2 = 0

rArr x = 0 (Note that sqrt(0) = 0)

Hence, we can write the x-intercept as (0,0)

color(green)(Step.3)

How do we find the Axis of Symmetry?

x-coordinate of the Vertex is the Equation of the Axis of Symmetry of the Parabola.

Axis of Symmetry is x= 0

We can easily verify all the above results in the graph.

I hope you find the graph and associated explanation useful.