Question

Graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts.
y= (x-2)(x-6)

Answer 1

y= (x-2)(x-6)
y becomes zero when x = 2 or x = 6. Those are the x-intercepts.
Therefore, the quadratic function will cut the x axis at x = 2 and at x = 6.

You can multiply it out, complete the square to put it in the vertex form. Can you take it from here?

Answer 2

y= (x-2)(x-6)
Multiply it out using FOIL:
y = x^2 - 6x - 2x + 12
y = x^2 - 8x + 12
complete the square:
y = (x - 4)^2 - 16 + 12
y = (x - 4)^2 - 4
compare it to the general vertex form: y = a(x-h)^2 + k where (h,k) is the vertex.

Here (4, -4) is the vertex.

This is an upward opening, vertical parabola and therefore the axis of symmetry will be a vertical line passing through the vertex and its equation will be x = 4.

With these info you can plot the points 2 and 6 on the x-axis. Plot the vertex at (4,-4) and draw a vertical parabola that opens upwards, has the minimum point at (4,-4) and pass through the two x-intercepts.

You cal also draw a vertical line passing through the vertex and label it the axis of symmetry.