Question

Graph the quadratic y=3x2−3
. What is the vertex of this quadratic?(1 point)
Responses

(−1,0)
left parenthesis negative 1 comma 0 right parenthesis

0
0

(0,−3)
left parenthesis 0 comma negative 3 right parenthesis

(1,0)

Answer 1

To find the vertex of the quadratic \( y = 3x^2 - 3 \), we can rewrite this equation in vertex form or identify characteristics directly from it.

1. **Standard Form**: The equation is already in standard form, which is \( y = ax^2 + bx + c \). Here, \( a = 3 \), \( b = 0 \), and \( c = -3 \).

2. **Finding the Vertex**: The vertex \( (h, k) \) of a parabola given in the form \( y = ax^2 + bx + c \) can be found using the formula:
\[
h = -\frac{b}{2a}
\]
Substituting in the values:
\[
h = -\frac{0}{2 \cdot 3} = 0
\]
Now we substitute \( h \) back into the equation to find \( k \):
\[
k = 3(0)^2 - 3 = -3
\]

3. **Vertex**: Thus, the vertex of the quadratic \( y = 3x^2 - 3 \) is \( (0, -3) \).

Therefore, the correct response is:
**(0, −3)**.