Question

What is the vertex of m(x) = -2(x-3)(x-9)

Answer 1

Answer:

Vertex: (6, 18)

Step-by-step explanation:

Given the quadratic function, m(x) = -2(x - 3)(x - 9):

Perform the FOIL method on the two binomials, (x - 3)(x - 9) without distributing -2:

m(x) = -2[(x - 3)(x - 9)]

Combine like terms:

m(x) = -2(x² - 9x - 3x + 27)

m(x) = -2(x² - 12x + 27)

where: a = 1, b = -12, and c = 27

Since the axis of symmetry occurs at x = h, then we can use the following formula to solve for the x-coordinate (h ) of the vertex, (h, k):

$x = \frac{-b}{2a}$

Substitute a = 1 and b = -12 into the formula:

$x = \frac{-b}{2a}$

$x = \frac{-(-12)}{2(1)} = \frac{12}{2} = 6$

Therefore, the x-coordinate (h) of the vertex is 6.  

Next, substitute the value of h into x² - 12x + 27 to find the y-coordinate (k ) of the vertex:

k = x² - 12x + 27

k = (6)² - 12(6) + 27

k = 36 - 72 + 27

k = 18

Therefore, the vertex of the quadratic function occurs at point (6, 18), in which it is the maximum point on the graph.