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rdesmangles

Answer:

Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola

The vertex of a parabola is the point at the top or bottom of the parabola

Step-by-step explanation:

Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f(x) = ax2 + bx + c by its full statement.

#1

  • y=a(x-h)²+k
  • y=a(x²)+3

Put (2,-5)

  • -5=2²a+3
  • -5=4a+3
  • 4a=-8
  • a=-2

Equation

  • y=-2(x-0)²+3

#2

  • y=a(x-2)²

Put (5,9)

  • 9=a(5-2)²
  • 3²a=9
  • 9=9
  • a=1

Equation

  • y=(x-2)²+0

#3

  • y=a(x+3)²+2

put (-1,14)

  • 14=a(2)²+2
  • 14=4a+2
  • 4a=12
  • a=3

Equation

  • y=3(x+3)²+2

#4

  • y=a(x-5)²-3

Put (1,-8)

  • -8=a(-4)²-3
  • -8=16a-3
  • 16a=-5
  • a=-5/16

Equation

y=-5/16(x-5)²-3

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