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:

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

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:

$-\frac{b}{2a}=-\frac{14}{2(1)}=-\frac{14}{2}=-7$

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)