The easiest way to test the bond strength of bars in a laboratory is by the pull-out test.

Find the vertex of the graph of the function. (5 points) f(x) = -2×2 – 16x – 34  

Assuming Vs does not exceed 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 31 in., b2 = 15 in., d1 = 4 in., and d2 = 53 in. There are three No. 7 longitudinal tension bars and No. 5 stirrups at 10 in. o.c.

Find a cubic function with the given zeros. (5 points)-7, 5, -3 

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. (5 points)

Do stirrups prevent inclined cracks from forming?

Find the zeros of the polynomial function and state the multiplicity of each. (5 points) f(x) = 3(x + 7)2(x – 7)3  

Assuming Vs exceeds 4sqrt(f’c)bwd, the maximum spacing for vertical stirrups in the following beam is _____. Let b1 = 37 in., b2 = 12 in., d1 = 6 in., and d2 = 33 in. There are three No. 8 longitudinal tension bars and No. 4 stirrups at 10 in. o.c.

Use synthetic division to determine whether the number k is an upper or lower bound (as specified for the real zeros of the function f). k = 2; f(x) = 2×3 + 4×2 + 2x – 4; Lower bound? (5 points)

No Eating or Drinking: Do not bring food and beverages to class. Food and beverages should NOT be consumed in the lab to prevent contamination of samples and equipment.