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!
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
Either way thank you!
Which quadratic rule represents the data in the table?
X|-1|0|1|2|3
Y|4|5|4|1|-4
The quadratic rule that represents the given data is:
y = -x^2 + 2x + 5
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
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.
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
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.
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
The quadratic rule that represents the given data is:
y = x^2 - 5
step by step pls
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