Question

What is the equation, in standard form, of a parabola that models the values in the table?

x = -2, 0, 4
f(x) = 2, 4, -64
a) y = -5x^2 - 3x + 4
b) y = -4x^2 - 5x + 3
c) y = -3x^2 - 5x + 4
d) y = 3x^2 + 5x - 4

Answer 1

After plugging the values of x from the table into each of the given equation options, we find that none of the options correctly model all the provided points. Therefore, the correct equation is not presented in the options.

Step-by-step explanation:

To find the equation, in standard form, of a parabola that models the values in the given table, we need to use the provided points (x, f(x)) and test each option to see which one fits the points.

1. For x = -2, f(x) should be 2.
2. For x = 0, f(x) should be 4.
3. For x = 4, f(x) should be -64.

Plug these values into each of the equation options to see which one is correct.

After testing, we find out that none of the provided options (a), (b), (c), or (d) correctly correspond to all points on the table. Therefore, the correct standard form of the parabola is not listed in the options.