Question

Find the coordinates of the vertex of the following parabola algebraically write your answer as an (x,y) point. Y=3x^2+9

a) (-3, 0)
b) (0, 9)
c) (3, 18)
d) (0, 3)

Answer 1

The vertex of the parabola given by the equation y = 3x^2 + 9 is at the point (0, 9).

Step-by-step explanation:

The task is to find the coordinates of the vertex of the parabola given by the equation y = 3x^2 + 9. This is a quadratic equation in standard form y = ax^2 + bx + c, where a is the coefficient of x2. In the given equation, there is no x term, so b = 0, and c = 9. This indicates that the parabola opens upwards with the coefficient of 3 being positive.

The vertex of a parabola in the form y = ax^2 occurs at the point (0, c) when b = 0. Therefore, for this equation, the vertex is at the point (0, 9).