Question

Which parabola has the graph shown?

A. (x-3)= (y+ 2)²
B. (x+4)= (y + 1)²
c. (x+7)² = (y + 2)
D. (x+3)=(y+ 1)²

Answer 1

first off, we're making an assumption on the distance from the directrix to the vertex.

now, the vertex or U-turn is at (-4 , -1) from the picture above, now, we can more or less assume that the distance from the vertex to the directrix or focus point, the distance "p" is 0.25 or a quarter of a unit, from the same picture, so p = 1/4, and is positive since the parabola is opening to the right.

`\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill`

`\begin{cases} h=-4\\ k=-1\\ p=(1)/(4) \end{cases}\implies 4((1)/(4))(~~x-(-4)~~) = (~~y-(-1)~~)^2 \\\\\\ 1(x+4)=(y+1)^2\implies {\Large \begin{array}{llll} (x+4)=(y+1)^2 \end{array}}`