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How do I find the x intercepts and vertex of y=(x+3)(x+5)-​

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Answer:

See below ~

Explanation:

Finding the x-intercepts :

  • y = 0 is the condition for an x-intercept
  • 0 = -(x + 3)(x + 5)
  • x + 3 = 0 ⇒ x = -3
  • x + 5 = 0 ⇒ x = -5
  • The x-intercepts are : (-3, 0) and (-5, 0)

Finding the vertex :

  • Expand the polynomial
  • y = -(x + 3)(x + 5)
  • y = -(x² + 3x + 5x + 15)
  • y = -(x² + 8x + 15)
  • y = -x² - 8x - 15
  • Vertex = (h, k)
  • h = -b/2a = 8/2(-1) = -4
  • k = -D/4a
  • k = -(-4 + 3)(-4 + 5)
  • k = -(-1)(1)
  • k = 1
  • The vertex is : (-4, 1)
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