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1.- What type of parabola is this?

2.- What is the vertex for the parabola?

3.- What is the 'a' value for the given graph?

4.- What is the equation for the given parabola?​

1 What type of parabola is this 2 What is the vertex for the parabola 3 What is the a value for the given graph 4 What is the equation for the given parabola class=

Respuesta :

semsee45

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:

[tex]x=a(y-k)^2+h[/tex]    

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:

[tex]\implies -1=a(2-1)^2-3[/tex]

[tex]\implies -1=a-3[/tex]

[tex]\implies a=2[/tex]

Part 4

Equation for the given parabola in vertex form:

[tex]x=2(y-1)^2-3[/tex]

Equation in standard form:

[tex]x=2y^2-4y-1[/tex]

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