Answer:
See below ~
Explanation:
Solving :
(a) Coordinates of P and Q
⇒ Equate the lines' equations
⇒ 2x² - 6x - 8 = 2x - 14
⇒ 2x² - 8x + 6 = 0
⇒ x² - 4x + 3 = 0
⇒ (x - 3)(x - 1) = 0
⇒ x = 3 and x = 1
Substitute each x-value in the any of the 2 equations :
⇒ y = 2(3) - 14
⇒ y = 6 - 14
⇒ y = -8
⇒ P = (3, -8)
⇒ y = 2(1) - 14
⇒ y = 2 - 14
⇒ y = -12
⇒ Q = (1, -12)
(b)
(i) 2x² - 6x - 8 = 0
⇒ x² - 3x - 4 = 0
⇒ (x - 4)(x + 1) = 0
⇒ x = 4 and x = -1
(ii) 2x² - 6x = -4
⇒ 2x² - 6x + 4 = 0
⇒ x² - 3x + 2 = 0
⇒ (x - 1)(x - 2) = 0
⇒ x = 1 and x = 2
(c) Line of symmetry
Finding the vertex :
⇒ Vertex = (h, k)
⇒ h = -b/2a
⇒ h = -(-6)/2(2)
⇒ h = 6/4
⇒ h = 1.5
⇒ The axis of symmetry's equation is : x = 1.5
(d)
⇒ As the mentioned function is a quadratic function, irrational values such as √2, √3, √6, etc. cannot be taken into consideration