Question

What are the vertex and axis of symmetry of the parabola: y = x^2 - 4x + 6?

a) Vertex: (2, 2); axis of symmetry: x = 2
b) Vertex: (-2, 2); axis of symmetry: x = -2
c) Vertex: (-2, 2); axis of symmetry: x = 2
d) Vertex: (2, -2); axis of symmetry: x = -2

Answer 1

The vertex of the parabola is (2, 2) and the axis of symmetry is x = 2.

Step-by-step explanation:

The given equation is y = x^2 - 4x + 6.

First, let's find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2.

Substituting the x-coordinate of the vertex into the equation, we can find the y-coordinate of the vertex. y = (2)^2 - 4(2) + 6 = 4 - 8 + 6 = 2.

Therefore, the vertex of the parabola is (2, 2).

Since the parabola is symmetric with respect to the axis of symmetry, which passes through the vertex, the equation of the axis of symmetry is x = 2.