Tell whether the graph opens up or down. Find the coordinates of the vertex. Write an equation of the axis of symmetry.

Y=3x^2

The graph opens up but I don't get how you would find the coordinates of vertex and how to write the equation of axis of symmetry.
Please help!

To determine whether the graph of the equation Y = 3x^2 opens up or down, we can look at the coefficient of the x^2 term.

In this case, the coefficient is positive (3), so the graph opens upwards. If the coefficient had been negative, the graph would open downwards.

To find the coordinates of the vertex, we can use the equation:

x-coordinate of the vertex = -b / (2a)

In our equation Y = 3x^2, the coefficient of x^2 is 3, so a = 3. Since there is no x term, b = 0.

x-coordinate of the vertex = -0 / (2 * 3) = 0

Substituting the x-coordinate of the vertex (0) back into the equation, we can find the y-coordinate:

Y = 3(0)^2 = 0

So, the coordinates of the vertex are (0, 0).

The equation of the axis of symmetry is x = ___.

The axis of symmetry is a vertical line that passes through the vertex. In this case, since the x-coordinate of the vertex is 0, the equation of the axis of symmetry is x = 0, or simply x = 0.

To determine whether the graph opens up or down for the quadratic function Y = 3x^2, we can look at the coefficient of x^2. In this case, the coefficient is positive, which means the graph opens upwards.

To find the coordinates of the vertex, we need to use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form of ax^2 + bx + c. In the given equation Y = 3x^2, a = 3, b = 0 (since there is no x term), and c = 0 (since there is no constant term).

Substituting these values into the formula:
x = -b/2a
= -0/2(3)
= 0

The x-coordinate of the vertex is 0. To find the corresponding y-coordinate, we substitute 0 into the equation:
Y = 3(0)^2
= 3(0)
= 0

Therefore, the vertex coordinates for the given quadratic equation Y = 3x^2 are (0, 0).

To write the equation of the axis of symmetry, we simply write x = (x-coordinate of the vertex). In this case, x = 0. Thus, the equation of the axis of symmetry is x = 0.