Question

Type the correct answer in the box.

Consider the table below.
х у
-3 0.5
-2
1
-1 2.5
0
5
18.5
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.

Answer 1

Explanation:

Use the standard form equation along with 3 of the coordinates from the table. I used (-1, 2.5), (0, 5), and (1, 8.5). Begin always with the coordinate where you have a 0:

`5=a(0)^2+b(0)+c` and we get immediately that c = 5. We can use that value as move forward with the next coordinate pair.

`8.5=a(1)^2+b(1)+5` and

8.5 = a + b + 5 and

3.5 = a + b Hold that thought while we come up with the second equation for this system.

`2.5=a(-1)^2+b(-1)+5` and

2.5 = a - b + 5 and

-2.5 = a - b Now solve this system using the method of eliination:

a + b = 3.5

+ a - b = -2.5

so

2a = 1 and a = 1/2 Now we can plug that in and solve for b:

a + b = 3.5 becomes

1/2 + b = 3.5 so

b = 3 and the equation is

`y=(1)/(2)x^2+3x+5`