Question

Could someone please answer question b) ii) ? The question is on the attached image.

Answer 1

Answer:

b) i) Curve A

ii) - 1.75

iii) x = 1 - √5  or x = 1 + √5

Step-by-step explanation:

b) i) We are given a function y = x² - 2x - 3 and the graph of this function is also shown in the side diagram.

The equation can be rearranged to y = (x - 1)² - 4

⇒ (x - 1)² = y + 4

Therefore, this is an equation of a parabola having the vertex at (1,-4) point and its axis is parallel to the positive y-axis.

So, the curve A represents the equation given. (Answer)

ii) Now, at x = 2.5, f(x) = 2.5² - 2 × 2.5 - 3 = - 1.75 (Answer)

iii) When y = 1, then x² -2x - 3 = 1

⇒ x² - 2x - 4 = 0

⇒ (x - 1)² - 5 = 0

⇒ (x - 1)² - (√5)² = 0

⇒ (x - 1 + √5)(x - 1 - √5) = 0

⇒ x = 1 - √5  or x = 1 + √5 (Answer)