Question

What is the axis of symmetry and vertex for the graph `y= -3x^2 + 4`?

Answer 1

The y-axis is the axis of symmetry and vertex is (0;4)

Explanation:

You should notice that:
1.) It is a quadratic (`x^2`) and therefore the graph is a parabola.
2.) The value of `a` is -3, therefore the parabola is 'upside down' and has a maximum turning point.
3.) There is no `x` term, therefore the parabola has not moved to the left or right, it is symmetrical about the y-axis which is then the axis of symmetry. (the line `x` = 0)
4.) The constant term, `c`, has the value 4, which is the y-intercept. The parabola has been moved 4 units upwards.
All points on the y-axis have the form (0;y)

Hence the vertex, or turning point, is the point (0,4).