Question

A. 2
B. 1/3
C. 5
D. -3​

Answer 1

Answer: 2

Step-by-step explanation:

$y=\frac{1}{3}x^2 +2x+5 \longrightarrow \frac{dy}{dx}=\frac{2}{3}x+2$

Setting this equal to 0 yields $x=-3$.

When $x=-3$, $y=2$

Answer 2

Answer:

• A. 2

Step-by-step explanation:

Given quadratic equation:

• y = (1/3)x² + 2x + 5

Its leading coefficient is positive, so it has minimum value at vertex.

The x-coordinate of the vertex is:

• x = -b/(2a)

Substitute the coefficients:

• x = - 2/(2*1/3) = - 3

Find the value of y at vertex:

• y = (1/3)(-3)² + 2(- 3) + 5 = 3 - 6 + 5 = 2

The matching answer choice is A.