Question

The graph of the function y=x2 + 5x + 6 has a A) Downward B) Upward

Answer 1

Answer:

B

Step-by-step explanation:

Given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 )

• If a > 0 then the graph opens upwards

• If a < 0 then the graph opens downwards

y = x² + 5x + 6 ← is in standard form

with a = 1 > 0

The graph therefore opens upward

Answer 2

on differentiating,

$\frac{dy}{dx} = 2x + 5$

on 2nd differentiating,

$\frac{ {d}^{2}y }{ {dx}^{2} } = 2$

since it's positive it's minimum and that means it points upwards.