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Answer:
smaller (t) = 2 and this in coordinates form (2,0)
larger (t) = 15 and this in coordinates form (15,0)
the vertex of the parabola = or in decimals (8.5, 42.25)
Step-by-step explanation:
- For the zeros of the function take each bracket and make it equal to zero.
SMALLER (t):
(t-2)=0
(add 2 for both sides)
t=2
LARGER (t):
(t-15)=0
(add 15 for both sides)
t=15
- For the vertex of the parabola you do:
step1: expand the brackets:
f(t)=-(t-2)(t-15)
f(t)=
step2: define a,b and c using the expression :
a= -1 (the coefficient of )
b= 17 (the coefficient of t)
c= -30 (the single number without a letter)
step3: sub the values in the formula to find the x coordinate of the vertex :
=
= or in decimals 8.5
step4: sub the value of t (the x-coordinate) in equation f(t):
f(t)=
f ( ) = -
+ 17×
- 30
= +
-30
= or in decimals 42.25
(THIS IS A PICTURE OF THE GRAPH↓)
