Hi,
What point is the intersection of the graphs:
x^2 + y = 2
y = -x^2 +2 Parabola V(0,2) opening downward (See below)
-y^2 + 3x = 2
x = (1/3)y^2 + 2/3 Parabola V(2/3,0) opening to the right (See below)
y = -x Line: Pt(0,0) slope m = -1 (slants left)
algebraically: substituting -x for y
x^2 -x - 2 = 0 = (x+1)(x-2)= 0, x = - 1(Extraneous) and x = 2
x = 2 then y = -2
Graphs: parabolas and Line intersect at:(2,-2)
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 and a and b are the respective vertices 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 )