Question

F(t) = -(t-2) (t-15)

Answer 1

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 =  $(\frac{17}{2} ,\frac{169}{4} )$ 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)= $-t^{2} +17t-30$

step2: define a,b and c using the expression $ax^{2} +bx+c$ :

a= -1 (the coefficient of $t^{2}$ )

b= 17 (the coefficient of t)

c= -30 (the single number without a letter)

step3: sub the values in the formula $-\frac{b}{2a}$ to find the x coordinate of the vertex :

$-\frac{b}{2a}$

= $- \frac{17}{2*-1}$

= $\frac{17}{2}$ or in decimals 8.5

step4: sub the value of t (the x-coordinate) in equation f(t):

f(t)= $-t^{2} +17t-30$

f ( $\frac{17}{2}$)  = - $(\frac{17}{2} )^{2}$+ 17× $\frac{17}{2}$ - 30

= $-\frac{289}{4}$ + $\frac{289}{2}$ -30

=$\frac{169}{4}$ or in decimals 42.25

(THIS IS A PICTURE OF THE GRAPH↓)