Respuesta :

fieryanswererft

Explanation:

f(x) = (x-4)(x+2)

1) For x-intercept, y will be 0

  • (x-4)(x+2) = 0
  • (x-4) =0, (x+2) = 0
  • x = 4, x = -2

x-intercept: (4, 0), (-2, 0)

2) For vertex: x = -b/2a where ax² + bx + c

Quadratic function:

  • (x-4)(x+2)
  • x² +2x-4x -8
  • x² -2x -8

vertex:

  • x = -(-2)/2(1)
  • x = 1

y: (x-4)(x+2) = (1-4)(1+2) = -9

ordered pair of vertex: (1, -9)

3) For y-intercept, x will be 0

  • (x-4)(x+2)
  • (0-4)(0+2)
  • -8

y-intercept: (0, -8)

Answer:

  1. (4, 0) and (-2, 0)
  2. (1, -9)
  3. (0, -8)

Step-by-step explanation:

Q1 : Finding x-intercepts

  • Take f(x) to be 0, because the intercepts lie on the x-axis
  • 0 = (x - 4)(x + 2)
  • x = 4 and x = -2
  • The x-intercepts are : (4, 0) and (-2, 0)

Q2

  • Coordinates of vertex are : (h, k)
  • Expand the polynomial
  • x² - 2x - 8
  • h = -b/2a = 2/2 = 1
  • k = -D/4a
  • D = b² - 4ac = 4 - 4(1)(-8) = 4 + 32 = 36
  • k = -36/4 = -9
  • The vertex is : (1, -9)

Q3

  • Take x = 0
  • y = 0² - 2(0) - 8
  • y = -8
  • y-intercept is : (0, -8)

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