For the function fx x2 2x 15 If x 3 what is f x If f x

For the function f(x) = x^2 - 2x - 15, If x = -3, what is f (x)? If f (x) = -7, what is x? Find the x intercepts and write them as two ordered pairs: Find the y intercept and write as an ordered pair:

Solution

6. We have f(x) = x² -2x-15.

(a). If x = -3, f(x) = (-3)² -2(-3)-15= 9 +6-15 = 0

(b) If f(x) = -7, then x² -2x-15 = -7 or, x² -2x-15+7 = 0 or, x² -2x-8 = 0 or x² -4x +2x-8 = 0or x(x-4)+2(x-4) = 0 or, (x-4)(x+2) = 0. Hence either x = 4 or x = -2.

(c ). The x –intercepts of f(x) are where f(x) = 0. Then x² -2x-15 = 0 or, x² -5x+3x-15= 0 or, x(x-5)+3(x-5) = 0 or, (x-5)(x+3) = 0. Thus, the x –intercepts of f(x) are (-3,0) and (5,0).

(d). The y –intercept of f(x) is where x = 0. Therefore, for the y-intercept of f(x) , we have y = f(x) = 0-0-15 = -15. Thus, the only y-intercept of f(x) is (0,-15).