Answer: y = -1*x^2 - 4
Step-by-step explanation:
A generic quadratic equation is written as:
y = a*x^2 + b*x + c
we need to find the values of a, b, and c
We have the table:
x y = f(x)
-4 -20
-3 -13
-2 -8
-1 -5
0 -4
1 -5
In the table we can see two things:
y(0) = a*0^2 + b*0 + c = c = -4
Then we know that:
y(x) = a*x^2 + b*x - 4
Now we only need to find a and b.
We also can see that we have symmetry around the point x = 0, this means that x = 0 is the vertex of the quadratic equation, and for a general case the vertex is at:
x = -b/2a
and this is equal to zero:
-b/2a = 0
then we must have b = 0.
So for now, the equation is:
y = a*x^2 -4
Now we can just replace the values of any of the points to find the value of a, for example we can use the point (1, -5)
this means that:
y = -5 = a*1^2 - 4
-5 = a - 4
-5 + 4 = a
-1 = a
Then the quadratic equation is:
y = -1*x^2 - 4
