THINKING 4. Given is the Linear and Quadratic System g(x) = 3x2 + 8x + k and f(x) = 2x – 1.
Determine k such that g(x) = 3x2 + 8x + k intersects f(x) = 2x – 1 at one point.

k = 2

Step-by-step explanation:

Given the equations:

g(x) = 3x² + 8x + k

f(x) = 2x - 1

At the intersection point:

g(x) = f(x)

3x² + 8x + k = 2x - 1

3x² + 6x + (k+1) = 0

If there is only one intersection point, the discriminant must be equal to zero:

b² - 4(a)(c) = 0

6² - 4(3)(k+1) = 0

36 - 12(k+1) = 0

36 - 12k - 12 = 0

24 = 12k

24/12 = k

2 = k

21

step-by-step explanation: