Hello need help with this one to and thanks and have a great day or weekend and be safe

a) It's a quadratic

b) f(x) = A(x-3)(x-7)

c) she is right

Step-by-step explanation:

(0-12)/(3-1) = -6

(-4-0)/(5-3) = -2

Since the slope is not constant, it can't be a linear.

Therefore a quadratic

Since the zeroes are 3 and 7,

Factors are (x - 3) and (x - 7)

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

Use any one point besides the x-intercepts to find A

12 = A(1-3)(1-7)

12 = 12A

A = 1

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

f(x) = x² - 7x - 3x + 21

f(x) = x² - 10x + 21

She is right