Question

1.- What type of parabola is this?

Answer 1

Answer:

Part 1

Sideways or "horizontal" parabola with a horizontal axis of symmetry.

Part 2

The vertex is the turning point:  (-3, 1)

Part 3

Vertex form of a horizontal parabola:

$x=a(y-k)^2+h$    

where:

• (h, k) is the vertex
• a is some constant
  If a > 0 the parabola opens to the right.
  If a < 0 the parabola opens to the left.

Point on the curve:  (-1, 2)

Substituting the vertex and the found point into the formula and solving for a:

$\implies -1=a(2-1)^2-3$

$\implies -1=a-3$

$\implies a=2$

Part 4

Equation for the given parabola in vertex form:

$x=2(y-1)^2-3$

Equation in standard form:

$x=2y^2-4y-1$