Hi,
y = x^2 + 6x - 4 This is a Parabola.
the vertex form of a parabola opening up or down, where(h,k) is the vertex.
y = x^2 + 6x - 4 |Completing the Square
y = (x+3)^2-9-4
y = (x+3)^2 - 13 Vertex(-3,13)
0 = (x+3)^2 - 13 | x = -3 ± sqrt(13), Roots -6.61 and .61
See below descriptions of various conics
Standard Form of an Equation of a Circle is
where Pt(h,k) is the center and r is the radius
Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center.
a and b are the respective vertices distances from center and ±are the foci distances from center
Standard Form of an Equation of an Hyperbola opening right and left is:
where Pt(h,k) is a center with vertices 'a' units right and left of center.
Standard Form of an Equation of an Hyperbola opening up and down is:
where Pt(h,k) is a center with vertices 'b' units up and down from center.
the vertex form of a parabola opening up or down, where(h,k) is the vertex.
The standard form is , where the focus is (h,k + p)
the vertex form of a parabola opening right or left, where(h,k) is the vertex.
The standard form is , where the focus is (h +p,k )