(0,3), (4,15), (5,33), determine the equation of the parabola they represent. State the direction the parabola opens.

y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.

Step-by-step explanation:

The general equation of a parabola is:

y = ax² + bx + c

So we have to solve for a, b and c to get our equation with the 3 given points.

When x = 0 and y = 3 we have

3 = a(0)² + b(0) + c, this means c = 3

When x = 4 and y = 15

15 = a(4)² + b(4) + 3 we have

16a + 4b = 12 which is

4a + b = 3

When x = 5 and y = 33 we have

33 = a(5)² + b(5) + 3 we have

25a + 5b = 30 which gives

5a + b = 6.

We have two equations

4a + b = 3

5a + b = 6

Eliminating b we have

a = 3, substituting a = 3 in the first equation we have

4(3) + b = 3

12 + b = 3

b = –9

Our equation therefore is:

y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.

$12. that is my answer.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|