What are the points of intersection of the two functions

Question

f(x)=-4x^2+3 g(x)=11x+9.

Answer 1

The two functions are f(x) = - 4x² + 3 and g(x) = 11x + 9

Rewrite the functions as y = - 4x² + 3 and y = 11x + 9

Equate the functions.

- 4x² + 3 = 11x + 9

- 4x² + 3 - 11x - 9 = 0

- 4x² - 11x - 6 = 0

4x² + 11x + 6 = 0

4x² + 8x + 3x + 6 = 0

4x(x + 2) + 3(x + 2) = 0

(x + 2)(4x + 3) = 0

x + 2 = 0 and 4x + 3 = 0

x = -2 and x = -3/4

Substitute the above x values either of two functions.

Substitute x = - 2 in y = 11x + 9.

y = 11(-2) + 9

y = - 22 + 9

y = - 13

Substitute x = -3/4 in y = 11x + 9.

y = 11(-3/4) + 9

y = (-33/4) + 9

y = (- 33 + 36)/4

y = 3/4

Intersection points are (-2, -13) and (-3/4, 3/4).