# ${\text{Write an equation of a horizontal parabola with a vertex of }}\left( { - 1,1} \right){\text{ and a }} \\ {\text{y - intercept of }}\left( {0,2} \right). \\ \\$
${\text{Let the equation of the horizontal parabola is }}{\left( {y - h} \right)^2} = 4a\left( {x - k} \right) \\ {\text{because its y intercept is}}\left( {0,2} \right)\;{\text{which is right side of the parabola }} \\ {\text{i}}{\text{.e parabola is opening right side}}{\text{.}} \\ {\text{so the vertex of the parabola is }}\left( {k,h} \right) \\ {\text{So, compare the vertex from the given vertex}} \\ {\text{i}}{\text{.e }}\left( { - 1,1} \right) \\ \Rightarrow k = - 1,\;h = 1 \\ {\text{So, the equation of parabola is}} \\ {\left( {y - 1} \right)^2} = 4a\left( {x + 1} \right) \\ {\text{Now the y intercept is }}\left( {0,2} \right){\text{ which satisfy the parabola}} \\ \Rightarrow {\left( {2 - 1} \right)^2} = 4a\left( {0 + 1} \right) \\ \Rightarrow 1 = 4a \\ \Rightarrow {\text{Equation of parabola is}} \\ {\left( {y - 1} \right)^2} = x + 1 \\ {\text{So, this is your required equation}}{\text{.}} \\ {\text{NOTE: - In this type of problem first check from given condition parabola is opening which side,}} \\ {\text{ then satisfying the condition according to given problem statement you will get your answer}}{\text{.}} \\$