Y=-x^2+6x-4
Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

Explanation:

1. Equation:

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

Where:    

The axis of symmetry is the vertical line with equation:

Substitute  

Thus, the axis of symmetry is:

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

Use the quadratic equation:

5. Find the y-intercept

The y-intercet is the value of y when x=0: