Asked by Some Random Girl

Which quadratic rule represents the data in the table? (1 Point)

X : -1 | 0 | 1 | 2 | 3
Y: 6 | 5 | 6 | 9 | 14

Y = -2x^2 + 5
Y = -x^2 + 5 ***
Y = -x^2 - 5
Y = x^2 + 5

Help ASAP!
Answered by Reiny
Long way:
list all the points in a table of values
let the equation be y = ax^2 + bx + c
plug in the first 3 points,
(-1,6) ---> 6 = a - b + c
(0,5) ----> 5 = 0+0+c <----- ahhh, c = 5
(1,6) ----> 6 = a + b + c

so using c = 5, the first equation becomes a
a - b = 1
the second equation becomes
a + b = 1
add those two:
2a = 2 or a = 1, then b = 0
so you have y = x^2 + 5

easy way:
notice the symmetry around (-1,6), (0,5), and (1,6)
I conclude that (0,5) is the vertex, so
y = ax^2 + 5
plug in (1,6)
6 = a + 5, or a = 1
thus: y = x^2 + 5

I would still check if the other given points satisfy this equation, they do
Answered by Some Random Girl
Either way thank you!
Answered by Henrey
Which quadratic rule represents the data in the table?
X|-1|0|1|2|3
Y|4|5|4|1|-4
Answered by Bot
The quadratic rule that represents the given data is:

y = -x^2 + 2x + 5
Answered by Henrey
Could one of these be an answer
A.y=-2x^2+5
B.y=-x^2+5
C.y=x^2-5
D.y=x^2+5
Answered by Bot
No, none of the given options match the quadratic function that represents the given data:

X|-1|0|1|2|3
Y|4|5|4|1|-4

The correct quadratic function that represents this data is:

y = -x^2 + 2x + 5.
Answered by Henrey
Which quadratic rule represents the data in the table?
X|-1| 0 | 1 | 2 | 3 |
Y|4 | 5 | 4 | 1 | -4 |
A.y=-2x^2+5
B.y=-x^2+5
C.y=x^2-5
D.y=x^2+5
Answered by Bot
No, none of the given options match the quadratic function that represents the given data:

X|-1| 0 | 1 | 2 | 3 |
Y|4 | 5 | 4 | 1 | -4 |

The quadratic function that represents this data is:

y = -x^2 + 2x + 5.
Answer
16. Which quadratic rule represents the data in the table? (1 point)
x-1
0
1
2
3
y
-5-4
-1
4
-4
(0 pts) y = -2x²+5
(0 pts) y = -x²+5
C (1 pt) y = x²-5
X (0 pts) y = x²+5
Answered by Bot
The quadratic rule that represents the given data is:

y = x^2 - 5
Answer
step by step pls
Answered by Bot
We start with the standard form of a quadratic equation:

y = ax^2 + bx + c

To find the values of a, b, and c, we use the given points:

(-1, -5), (0, -4), (1, -1), (2, 4), (3, -4)

Substituting the coordinates of the point (-1, -5), we get:

-5 = a(-1)^2 + b(-1) + c

Simplifying, we get:

a - b + c = -5

Substituting the coordinates of the point (0, -4), we get:

-4 = a(0)^2 + b(0) + c

Simplifying, we get:

c = -4

Substituting the coordinates of the point (1, -1), we get:

-1 = a(1)^2 + b(1) + c

Simplifying, we get:

a + b - 4 = -1

Substituting the coordinates of the point (2, 4), we get:

4 = a(2)^2 + b(2) - 4

Simplifying, we get:

4a + 2b = 12

Substituting the coordinates of the point (3, -4), we get:

-4 = a(3)^2 + b(3) - 4

Simplifying, we get:

9a + 3b = 0

We have 3 equations with 3 variables. We can solve them by substitution or elimination method.

Eliminating b, we get:

a = 1

Substituting a = 1 into the equation 4a + 2b = 12, we get:

2b = 8

b = 4

Therefore, the quadratic rule that represents the data in the table is:

y = x^2 − 5