Question

graph the quadratic function f(x) = (x-3)^2 +3

Answer 1

Answer:

The axis of symmetry would run through the parabola's vertex, located at (-1, b), where b is a real number.

Let the parabolic function be f(x) = a(x + 1)^2 + b, where a, b are real numbers.

(0,3) and (-3, 9) being on the graph means

3 = f(0) = a (0 + 1)^2 + b = a + b

9 = f(-3) = a (-3 + 1)^2 + b = 4a + b

9 - 3 = (4a + b) - (a + b)

6 = 3a

a = 2

But a + b = 3

Thus 2 + b = 3, so b = 1

f(x) = 2 (x + 1)^2 + 1

f(x) = 2x^2 + 4x + 2 + 1

f(x) = 2x^2 + 4x + 3