Question

What is the axis of symmetry? What are the coordinates of the vertex?
y=6+2x-x²

Answer 1

Axis of Symmetry: x = 1

Vertex: (1,7)

Explanation:

The standard form of an equation for a parabola is

ax² + bx + c

So converted to standard form, the equation is

y = -x² + 2x + 6,

where

a = -1, b = 2, and c = 6

The axis of symmetry of a parabola follows the formula

x = -b/(2a)

--> x = -2/(2*(-1))

--> x = 1

This is also the x-coordinate of the vertex.

To get the y-coordinates of the vertex, substitute 1 into x:

y=6+2x-x²

y=6+2(1)-(1)²

y = 7

So the coordinates of the vertex is (1,7)