Question

Which of the following equations is of a parabola with a vertex at (1, -1)?

y = (x - 1)2 - 1
y = (x - 1)2 + 1
y = (x + 1)2 - 1
y = (x + 1)2 + 1

Answer 1

`\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ (1,-1)\implies \begin{cases} h=1\\ k=-1 \end{cases}\implies y=a(x-1)^2-1 \\\\\\ \textit{and if we assume \boxed{a=1} then}\implies y=(x-1)^2-1`