Question

Which equation could represent each graphed polynomial function PLEASE HELP FAST!!!

Answer 1

Answer:

y = x⁴- 5x² + 4

y = x(x + 3)(x - 2)

Step-by-step explanation:

1). y = x⁴- 5x² + 4

      = x⁴- 4x² - x² + 4

      = x²(x² - 4) - 1(x²- 4)

   y = (x² - 1)(x² - 4)

   y = (x - 1)(x + 1)(x - 2)(x + 2)

  Therefore, zeros of this polynomial are,

   x = -2, -1, 1, 2

   From the given graphs, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.

   So the graph (1) represents the polynomial → y = x⁴- 5x² + 4

2). Second graph shows the x-intercepts at x = -3, 0, 2

   Since, y = x(x + 3)(x - 2) is the polynomial with x intercepts at x = -3, 0, 2

   Therefore, y = x(x + 3)(x - 2) represents the second graph.