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)

f (x) = (x + 3) (x - 7)

f (x) = (x + 3) (x - 7)

Step-by-step explanation:

its d i had the test

"f (x) = (x + 3) (x - 7) "

Step-by-step explanation:

If the vertex is (h, k), then the quadratic is can be written in the form:

y = a (x-h) ^2 + k

So it will be:

y = a (x-2) ^2 - 25

Now, to find a, we need the x-intercept (which is 7), so we plug in 7 into x and 0 into y and solve for a:

0 = a (7-2) ^2 - 25

0 = a (5) ^2 - 25

0 = 25a - 25

a = 1

THus, we can write:

y = (x-2) ^2 - 25

Expanding this, we get:

y = x^2 - 4x + 4 - 25

y = x^2 - 4x - 21

y = (x-7) (x+3)

THis is correct answer.