Question

Consider f(x) = m(x-n)(x-2). The graph of y=f(x) has axis of symmetryx=4 and y-intercept at (0,-6).

find m and n​

Answer 1

To find m and n, we can use the information given. Since the axis of symmetry is x = 4, it means that the vertex of the parabola is at (4, k), where k is the y-coordinate of the vertex. Since the y-intercept is at (0, -6), we can substitute these values into the equation:

m(0 - n)(0 - 2) = -6

Simplifying this equation, we get:

2mn = -6

Since the vertex is on the axis of symmetry, we know that the x-coordinate of the vertex is equal to (n + 2)/2. So, we have:

(n + 2)/2 = 4

Simplifying this equation, we get:

n + 2 = 8

n = 6

Substituting the value of n into the equation 2mn = -6, we get:

2m(6) = -6

12m = -6

m = -6/12

m = -1/2

Therefore, m = -1/2 and n = 6.