Question

Graph these equations. identify the axis of symmetry, vertex and y-intercept

Answer 1

The given equation is

`y=(1)/(4)x^2+x-6`

The vertex has the form V(h,k), where

`h=-(b)/(2a),k=f(h)`

Where a = 1/4 and b = 1.

`\begin{gathered} h=-(1)/(2((1)/(4)))=-(1)/((1)/(2))=-2 \\ k=f(-2)=(1)/(4)(-2)^2+(-2)-6=(1)/(4)\cdot4-2-6 \\ k=1-8=-7 \end{gathered}`

Hence, the vertex is (-2,-7).

The axis of symmetry is x = -2.

The y-intercept would be -6 because that's the independent term.

The graph of this equation would be