Question

given the equation (x - 3)² + 5, name the vertex of the parabola

Answer 1

hello

to solve this question, let's expand the factored form and rewrite the equation

$\begin{gathered} y=(x-3)^2+5 \\ y=x^2-6x+9+5_{} \\ y=x^2-6x+14 \end{gathered}$

to find the vertex of a parabola, we can use the formula a/b from a quadratic equation

$\begin{gathered} y=x^2-6x+14 \\ a=1,b=-6,c=14 \end{gathered}$$\begin{gathered} \text{vertex}=\text{ a/b} \\ v=\frac{1}{-6} \end{gathered}$

from the calculation above, the vertex of the parabola is equal to -1/6