Question

hat are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36? (−4, 0) and (9, 0) (4, 0) and (−9, 0) (−3, 0) and (12, 0) (3, 0) and (−12, 0)

Answer 1

The x-intercepts of the function f(x) = x^2 + 5x - 36 are (-9, 0) and (4, 0), found by setting the function equal to zero and factoring the quadratic equation.

Step-by-step explanation:

The x-intercepts of a graph of a function are the points where the graph crosses the x-axis. For the function f(x) = x2 + 5x - 36, to find the x-intercepts, you set f(x) to zero and solve for x:

0 = x2 + 5x - 36

To solve this quadratic equation, we can factor it, if possible, or use the quadratic formula. Factoring the given quadratic equation, we get:

(x + 9)(x - 4) = 0

Setting each factor equal to zero gives us the solutions for x:

x + 9 = 0 or x - 4 = 0

So, x = -9 or x = 4. Therefore, the x-intercepts are (-9, 0) and (4, 0).