# What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola f(x)=x^2 -2x -15?

Jun 11, 2015

You can factorise: $= \left(x + 3\right) \left(x - 5\right)$

#### Explanation:

This gives you the zero-points $x = - 3 \mathmr{and} x = 5$
Halfway between these lies the axis of symmetry :
$x = \left(- 3 + 5\right) / 2 \to x = + 1$
The vertex is on this axis, so putting in $x = 1$:
$f \left(1\right) = {1}^{2} - 2.1 - 15 = - 16$
So the vertex $= \left(1 , - 16\right)$
Since the coefficient of ${x}^{2}$ is positive, this is a minumum
There is no maximum, so the range is $- 16 \le f \left(x\right) < \infty$
Since there are no roots or fractions involved the domain of $x$ is unlimited.
graph{x^2-2x-15 [-41.1, 41.1, -20.55, 20.52]}