Question

On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0). What is the range of the function on the graph? all the real numbers all the real numbers greater than or equal to 0 all the real numbers greater than or equal to 2 all the real numbers greater than or equal to –3

Answer 1

Answer:

all the real numbers greater than or equal to –3

y  =  x² - 4x + 1

Graph enclosed

Step-by-step explanation:

x           y

0           1

0.25      0

2           -3

3.75       0

y = ax² + bx + c

putting x = 0 & y = 1

1 = 0 + 0 + c

=> c = 1

y = ax² + bx + 1

putting x = 0.25 & y = 0

0 = a(0.25)²  + b(0.25) + 1

putting x = 3.75 & y = 0

=> 0 =  a(3.75)²  + b(3.75) + 1

Equating both

a(0.25)²  + b(0.25) + 1  = a(3.75)²  + b(3.75) + 1

=> -14a = b(3.5)

=> b = - 4a

y  = ax² - 4ax + 1

putting x = 2 & y = -3

=> - 3 = a*2²  -4a(2) + 1

=> -3 = 4a - 8a + 1

=> -- 4 = - 4a

=> a = 1

y  =  x² - 4x + 1

dy/dx =  2x - 4

dy/dx =  0  => x = 2  

d²y/dx² =  2   (+ ve) => x = 2 will give minimum value of y

which is - 3

the range of the function on the graph

all the real numbers greater than or equal to –3