Respuesta :

Answer:

See below ~

Step-by-step explanation:

(a) To find y-intercept :

  • y = -x² + 2x + 15
  • y = -(0)² + 2(0) + 15
  • y = 15
  • M is : (0, 15)

(b) Finding x-intercepts :

  • 0 = -x² + 2x + 15
  • -x² + 5x - 3x + 15 = 0
  • x(-x + 5) + 3(-x + 5) = 0
  • (x + 3)(-x + 5) = 0
  • x + 3 = 0 ⇒ x = -3
  • -x + 5 = 0 ⇒ x = 5
  • P and Q are : (-3, 0) and (5, 0)

(C) Finding vertex :

  • Vertex is (h, k)
  • h = -b/2a = -2/2(-1) = 1
  • k = -(1)² + 2(1) + 15
  • k = -1 + 2 + 15
  • k = 16
  • The maximum point is : (1, 16)
a) Make x=0
y= 15
M= (0,15)
b) Make y=0 and solve the quadratic equation
(x+3)(x-5)=0
x=-3, y=0
x=5, y=0
c) -b/2a
Max point coordinate= (1,16)

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