Question

The graph of the function f(x) is shown.

Enter a value of x where f(x) and the equation y = 0.5x + 3 intersect.

Answer 1

x = 2

x = -1.5

Explanation:

The graph is of function f(x) = x²

Therefore, to find where the function intersects with y = 0.5x + 3,

equal the functions and solve for x:

⇒ x² = 0.5x + 3

⇒ x² - 0.5x - 3 = 0

Multiply both sides by 2:

⇒ 2x² - x - 6 = 0

Factor:

⇒ 2x² - 4x + 3x - 6 = 0

⇒ 2x(x - 2) + 3(x - 2) = 0

⇒ (x - 2)(2x + 3) = 0

Therefore:

(x - 2) = 0 ⇒ x = 2

(2x + 3) = 0 ⇒ x = -1.5