Question

Determine the value of k such that g(x) = 3x + k intersects the quadratic function f(x) = 2x^2 - 5x + 3

Answer 1

The answer is supposed to be \[k \ge -5\]

Answer 2

and after I equated I got 2x^2 - 8x + 3-k

Answer 3

b^2 -4ac=0

Answer 4

and then I use the discriminat: (-8)^2 - 4(2)(3-k) = 64 - 8 - 12 but I don't know how to get the k.. is it +4k?

Answer 5

a=2 b=-8 c=3-k

Answer 6

f(x) = g(x)
2x^2 - 5x + 3 = 3x + k
2x^2 -8x +3-k = 0
the two graphs intersect when the quadratic has real solutions

64 - 8(3-k) >= 0
40 +8k >=0
k >= -5

Answer 7

(-8)^(2)-4(2)(3-k)=0

((64))-4(2)(3-k)=0

(64)-4(2)(3-k)=0

64-4(2)(3-k)=0

64-4(6-2k)=0

64-24+8k=0

40+8k=0

8k=-40

k=-5

Answer 8

ohhh so I multiply the ones with the brackets first?

Answer 9

yes