Question

The table of values forms a quadratic function f(x)

x f(x)
-1 24
0 30
1 32
2 30
3 24
4 14
5 0
What is the equation that represents f(x)?
Of(x) = -2x² + 4x + 30
Of(x) = 2x² - 4x-30
Of(x) = -x² + 2x + 15
Of(x)=x²-2x-15

Answer 1

the answer is A) -2x² + 4x + 30

Explanation:

To find the equation of the quadratic function f(x), we can use the standard form of a quadratic function: f(x) = ax^2 + bx + c, where a, b, and c are constants.

We can plug in the values of x and f(x) from the table to get three equations:

a(-1)^2 + b(-1) + c = 24

a(0)^2 + b(0) + c = 30

a(1)^2 + b(1) + c = 32

Simplifying each equation, we get:

a - b + c = 24

c = 30

a + b + c = 32

We can substitute c = 30 into the first and third equations to get:

a - b + 30 = 24

a + b + 30 = 32

Simplifying these equations, we get:

a - b = -6

a + b = 2

Adding these two equations, we get:

2a = -4

Dividing by 2, we get:

a = -2

Substituting a = -2 into one of the equations above, we get:

-2 - b = -6

Solving for b, we get:

b = 4

Therefore, the equation that represents f(x) is:

f(x) = -2x^2 + 4x + 30

So the answer is A) -2x² + 4x + 30