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

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

8 0

Answer: f(x) = (x + 3)(x – 7)

Step-by-step explanation: Use "standard form" of the function and insert values given: vertex (2,-25) intercept point (7,0)

f(x) = a(x-h)² + k from vertex, h is 2 y is -25 from intercept, x is 7 f(x) is 0

to find a, 0 = a(7-2)² +(-25) 0 = a(7-2)² -25 add 25 to both sides

25 = a(5)² 25 = 25a 25/25 = a 1=a (seems useless but verifies implied "a"coefficient is 1)

f(x) = a(x-h)² + k solve to get the quadratic form

f(x) = (x-2)² -25 (x - 2)² is x² -4x +4

f(x) = x² -4x +4 -25 simplify

f(x) = x² -4x - 21 then factor

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

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