Question

The graph of a quadratic function f(x) intersects the x-axis At -3 and 5. Create a function that would produce these results.

Answer 1

Answer:

f(x) = x² - 2x - 15

Step-by-step explanation:

∵ The function intersect x-axis at -3 and 5

∴ f(x) = 0 at x = -3 , 5

∵ The form of the quadratic equation is ⇒ ax² + -b/a x + c/a = 0

                                                                       ax² - b/a x + c/a = 0

Where the sum of its roots is b/a and their multiplication is c/a

∵ a = 1

∵ -3 , 5 are the roots of the quadratic equation

∴ b = -3 + 5 = 2

∴ c = -3 × 5 = -15

∴ f(x) = x² - 2x - 15