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A volleyball reaches its maximum height of 13 feet, 3 seconds after its served. Which of the following quadratics could model the height of the vollyball over time after it is served. Select all that apply.
A: f(x)=2x^2+12x+5
B: f(x)=-2x^2+12x-5
C: f(x)=-2x^2-12x+5
D: f(x)=-2(x-3)^2+13
E: f(x)=-2(x+3)^2+13

Respuesta :

carlosego
The first thing we must do in this case is to see which equations meet the following condition:
 "A volleyball reaches its maximum height of 13 feet, 3 seconds after its served"
 We have then:
 Equation 1:
 f (x) = - 2 (x-3) ^ 2 + 13
 f (3) = - 2 (3-3) ^ 2 + 13
 f (3) = 13
 Yes, meet the condition
 Equation 2:
 f (x) = - 2x ^ 2 + 12x-5
 f (3) = - 2 (3) ^ 2 + 12 (3) -5
 f (3) = - 18 + 36-5
 f (3) = 13
 Yes, meet the condition
 Answer:
 B: f (x) = - 2x ^ 2 + 12x-5
 D: f (x) = - 2 (x-3) ^ 2 + 13
f(x)=a(x-h)^2+k
Maximum point: Vertex: V=(h,k)=(3,13)→h=3, k=13
Opens downward, then a<0 (negative)
f(x)=a(x-3)^2+13, with "a" negative

Possible option:
D: f(x)=-2(x-3)^2+13
Developing this expression:
f(x)=-2[(x)^2-2(x)(3)+(3)^2]+13
f(x)=-2(x^2-6x+9)+13
f(x)=-2x^2+12x-18+13
f(x)=-2x^2+12x-5. This is Option B

Answer: 2 Options:
Option B: f(x)=-2x^2+12x-5    and
Option D: f(x)=-2(x-3)^2+13