SOLUTION: find the vertex, focus, and directrix of the parabola given by each equation. Sketch the graph. (y – 1)^2 = 2x + 8

Algebra ->  Length-and-distance -> SOLUTION: find the vertex, focus, and directrix of the parabola given by each equation. Sketch the graph. (y – 1)^2 = 2x + 8       Log On


   

Question 1052024: find the vertex, focus, and directrix of the parabola given by each equation. Sketch the graph.

(y – 1)^2 = 2x + 8
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Similar to your other question like this.

%28y-1%29%5E2=2%28x%2B4%29, simple factorization;

2%28x%2B4%29=%28y-1%29%5E2
This form and readable values should tell you that this parabola is of symmetry axis parallel to the x-axis, vertex point is a the far left of the graph and parabola opens to the right. (The parabola is HORIZONTAL).


Remember the equational form, 4p%28x-h%29=%28y-k%29%5E2 ?

Vertex, you read right from the equation: (-4,1).

p is distance between vertex and either the focus or directrix.
4p=2
p=1%2F2---------you can find from this, the focus and the directrix.