Question

What are the coordinates of the vertex of the quadratic function f(x) = x² + 2?

a) (0, 2)
b) (-2, 4)
c) (2, 4)
d) (-4, 6)
e) (4, 6)

Answer 1

The vertex of the quadratic function f(x) = x² + 2 is at the point (0, 2).

Step-by-step explanation:

The coordinates of the vertex of the quadratic function f(x) = x² + 2 can be found using the vertex formula for a quadratic equation of the form ax² + bx + c. In this equation, the coefficient a is 1 and the coefficient b is 0 (as there is no x term). The vertex of a quadratic function is at the point (-b/2a, f(-b/2a)).

Substituting the values of a and b into the vertex formula gives us:
-b/2a = -0/(2*1) = 0.
Thus, the x-coordinate of the vertex is 0. The y-coordinate is f(0), which is:
f(0) = 0² + 2 = 2.

Therefore, the vertex of the function is (0, 2).