# What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for y=x^2 - 3?

May 26, 2015

Since this is in the form $y = {\left(x + a\right)}^{2} + b$:

$a = 0 \to$axis of symmetry: $x = 0$

$b = - 3 \to$ vertex $\left(0 , - 3\right)$ is also the y-intercept
Since the coefficient of the square is positive ($= 1$) this is a so-called "valley parabola" and the $y$-value of the vertex is also the minimum.
There is no maximum, so the range: $- 3 \le y < \infty$

$x$ may have any value, so domain: $- \infty < x < + \infty$

The x-intercepts (where y=0) are $\left(- \sqrt{3} , 0\right) \mathmr{and} \left(+ \sqrt{3} , 0\right)$
graph{x^2-3 [-10, 10, -5, 5]}