Respuesta :

MathPhys

Answer:

y = (x − 2)² − 25

Step-by-step explanation:

Vertex form of a quadratic is:

y = a (x − h)² + k

where (h, k) is the vertex.

Given that h = 2 and k = -25:

y = a (x − 2)² − 25

And given that a point is (7, 0):

0 = a (7 − 2)² − 25

0 = 25a − 25

a = 1

Therefore, the equation is:

y = (x − 2)² − 25

Answer:

f(x) = x^2 - 4x - 21.

Step-by-step explanation:

Since the vertex is at (2, -25) we can write the vertex form as:

y = f(x) = a(x - 2)^2  -25

Given the x-intercept ( 7, 0),  x = 7 when y = 0, so substituting:

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

0 = 25a - 25

giving a = 1.

So our equation is f(x) = (x - 2)^2 - 25.

Converting to standard form

f(x) = x^2 - 4x + 4 - 25

f(x) = x^2 - 4x - 21.

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