Find the value of a that will make h(x) continuous

Question

2x²+ax+3 ; x < -4

3x+a ; x >= -4

Answer 1

2x^2 +ax + 3 = 3x+a

2(-4)^2 -4a +3 = -12 +a

32+3 +12 = 5a

5a = 47

a =47/5

Answer 2

For the whole function to be continuous, the two ends need to have the same value when they meet at x=-4. So, set each expression equal to each other, substitute -4 for x, and then solve for a:

2x² + ax + 3 = 3x + a

2(-4)² + a(-4) + 3 = 3(-4) + a

2(16) - 4a + 3 = -12 + a

35 - 4a = -12 + a

37 = 5a

a = 37/5 = 9.4

Answer 3

desmos.com/calculator/zsx7acartq