how do I Sketch a graph of f(x) where f(x)=x^2 -3?

Question

What is the vertex and what is the point?

Answer 1

Because the coefficient of x² is positive, the shape of the curve is a U-shaped parabola with the arms of the U slowly widening apart. The vertex is the minimum part of the U and intercepts the y-axis at y=-3. The parabola is symmetrical about the y-axis. The x intercepts are found by putting y=0, so x²-3=0 and the intercepts on the x-axis are at x=-√3 and x=√3. √3 is about 1.7, so when you are drawing the graph make sure all the intercepts look right and that the vertex is at (0,-3). Your picture should look something like the one below.