Given that the zeros of a quadratic function are –2 and 8, what is the standard form of the quadratic function?

To find the standard form of a quadratic function given its zeros, we can use the factored form of the quadratic function. If the zeros are ( r_1 ) and ( r_2 ), the quadratic function can be expressed as:

[ f(x) = a(x – r_1)(x – r_2) ]

Given the zeros are –2 and 8, we can plug these values in:

[ f(x) = a(x + 2)(x – 8) ]

Now let’s expand this:

1. First, expand the factors:

[

f(x) = a[(x + 2)(x – 8)] = a(x^2 – 8x + 2x – 16) = a(x^2 – 6x – 16)

]

2. By setting ( a = 1 ) (for the standard form), we get:

[

f(x) = x^2 – 6x – 16

]

So the standard form of the quadratic function is:

D ( f(x) = x^2 – 6x – 16 )

This choice matches the expanded expression, confirming it’s correct.