Question

Find the coordinates of the vertex of the graph of y=4-x^2 indentify the vertex as a maximum or minimum point A.(2,9);maximumB.(0,4);minimumC.(0,4);maximum D.(2,0);minimum

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} y=4-x^2 \\ y=-x^2+4 \\ a=-1,b=0,c=4 \\ x_v=-(b)/(2a)=-(0)/(2(-1))=0 \\ y_v=-(b^2-4ac)/(4a)=-(0^2-4(-1)(4))/(4(-1)) \\ y_v=-(0+16)/(-4)=(-16)/(-4)=4 \\ y_v=4 \\ \\ \therefore The\text{ vertex of the equation is }(0,4) \end{gathered}`

To know if the vertex is the maximum or minimum point, we will follow this below:

`\begin{gathered} y_v=4 \\ \Rightarrow This\text{ is a minimum point} \end{gathered}`

Hence, the answer is B.(0,4); minimum