Respuesta :
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