### Instruction: Find the focus of the parabola $y = 4x^2 - 3.$.### Response: I recall that the general equation of a parabola with vertical axis of symmetry is $y = a(x - h)^2 + k,$ where $(h, k)$ is the vertex and $a$ determines the shape and direction of the parabola.
To find the focus, I need to identify the vertex and the value of $a$ from the given equation.
I can rewrite the given equation as $y = 4(x - 0)^2 - 3,$ which tells me that the vertex is at $(0, -3)$ and $a = 4.$
Since $a$ is positive, the parabola opens upward.
I also remember that the distance from the vertex to the focus is $1/4a.$