Question

How do you identify the important parts of `y = x^2 - x - 2` to graph it?

Answer 1

The axis of symmetry is `x=1/2`.
The vertex is `(1/2,-2 1/4)`.

Explanation:

`y=x^2-x-2` is a quadratic equation of the form `ax^2+bx+c`, where `a=1, b=-1, and c=-2`.

Axis of Symmetry

The graph of a quadratic equation is a parabola. First find the axis of symmetry. This is the vertical line that divides the parabola in half. The formula for the axis of symmetry is `x=(-(b))/(2a)`.

`x=(-(b))/(2a)=(-(-1))/(2*1)=`

The axis of symmetry is `x=1/2`.

Vertex

Now find the vertex, which is the maximum or minimum point on the parabola. In this case it will be the minimum point. `x=1/2` is the `x` value for the vertex. To find the `y` value, substitute `1/2` for `x` in the equation and solve for `x`.

`y=(1/2)^2-1/2-2=`

`y=1/4-1/2-2=`

`y=1/4-2/4-8/4=`

`y=-2 1/4`

The vertex is `(1/2,-2 1/4)`.

Next determine some points by substituting values for `x` on both sides of the axis of symmetry. Plot the vertex and the other points. Sketch a parabola through the points. Do not connect the dots.

`x=-1,` `y=0`
`x=0,` `=-2`
`x=1/2,` `y=-2 1/4`
`x=1,` `y=-2`
`x=2,` `y=0`

graph{y=x^2-x-2 [-10, 10, -5, 5]}