Question

(Algebra 2) Find the vertex of this parabola. Use -b/2a to find x and then substitute your answer to find y.

Answer 1

We have that the vertex of a general quadratic equation is the following point:

`\begin{gathered} \text{Given:} \\ y=ax^2+bx+c \\ Vertex\colon(-(b)/(2a),_{}y(-(b)/(2a))) \end{gathered}`

in this case, we have the following:

`\begin{gathered} x^2+14x+44 \\ \text{then:} \\ a=1 \\ b=14 \\ c=44 \end{gathered}`

then, lets find the x-coordinate:

`-(b)/(2a)=-(14)/(2(1))=-(14)/(2)=-7`

then, evaluating -7 on the equation,we get:

`\begin{gathered} y(-7)=(-7)^2+14(-7)+44=49-98+44=-5 \\ \end{gathered}`

therefore, the vertex is (-7 , -5)