Free Response Questions
20. A quadratic function has a turning point at (3,8). Selected values for the function are shown in the table
below
(a) Finish filling out the table.
(b) State the zeroes of the function.

Step-by-step explanation:

let the quadratic function be y=ax^2+bx+c

when x=1,y=0

0=a+b+c   ...(1)

when x=3,y=8

8=9a+3b+c   ...(2)

when x=4,y=6

6=16a+4b+c  ...(3)

(2)-(1) gives

8a+2b=8

or 4a+b=4   ...(4)

(3)-(2) gives

7a+b=-2    ...(5)

(4)-(5) gives

-3a=4+2=6

a=-2

from (4)

4(-2)+b=4

b=4+8=12

from (1)

-2+12+c=0

10+c=0

c=-10

so y=-2x²+12x-10

when x=-1,y=-2(-1)²+12(-1)-10=-2-12-10=-24

when x=2,y=-2(2)²+12(2)-10=-8+24-10=6

when x=5,y=-2(5)²+12(5)-10=-50+60-10=0

when x=6,y=-2(6)²+12(6)-10=-72+72-10=-10

b. to find the zeroes

-2x²+12x-10=0

x²-6x+5=0

x²-x-5x+5=0

x(x-5)-1(x-5)=0

(x-5)(x-1)=0

x=5,1

so zeroes are at x=1,5

21.

f(x)=x²+4x-1

=x²+4x+4-4-1

=(x+2)²-5

it is an upward parabola with vertex at(-2,-5)

when x=-6,y=(-6+2)²-5=16-6=11

when x=-5,y=(-5+2)²-5=9-5=4

x=-4, y=(-4+2)²-5=4-5=-1

x=-3,y=(-3+2)²-5=1-5=-4

x=1,y=(1+2)²-5=9-5=4

x=2,y=(2+2)²-5=16-5=11

join these points you get the graph.

f(x) is increasing if f'(x)>0

f'(x)=2x+4

2x+4>0

x>-2

or -2≤x≤2

c. x=0 lies in the interval -2≤x≤2

or in f'(x)>0

also when x=0

f(x)=-1 or in f(x)<0

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.