Question

Please help

The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23

What is the equation of f(x)?
f(x) = (x − 5)2 − 2
f(x) = (x − 4)2 − 1
f(x) = (x + 4)2 − 1
f(x) = (x + 5)2 − 2

Answer 1

Explanation:

From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.

Our model is

`y=a(x-h)^2+k` where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:

`-1=a(-4+5)^2-2` and

`-1=a(1)^2-2` and

-1 = a - 2 so

a = 1.

Now we can fill in the equation with the coordinates of the vertex and the value found for a to get

`y=(x+5)^2-2` You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.