What is the equation of the quadratic function with a vertex at (2, 25) and an x-intercept at (7,0)?
f(x) = (x - 2)(x - 7)
f(x) = (x + 2)(x + 7)
f(x) = (x - 3)(x + 7)
of(x) = (x + 3)(x - 7)

which is none of the choices provided.

Are you sure the question is right or even the choices?

You can even write it as:

but this is still not a choice.

Step-by-step explanation:

The vertex form of a quadratic is .

This is called vertex form because it gives you the vertex is .

We are given that which makes our equation:

.

We can find the value of by plugging in the x-intercept (7,0) for into:

Subtract 25 on both sides:

Divide both sides by 25:

.

So the equation for the quadratic is:

Let's put this into factored form since all the choices are in factored form.

This will require us to multiply the (x-2)(x-2) out:

Factor out -1:

WE need to find two numbers that multiply to be -21 and add to be -4:

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation: