Quadratic Formula

1. Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work.

x2 + 4x + 13 = 0
2. 2. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.

x2 + 10x + 19 = 0
a. Two different imaginary solutions
b. Two different rational solutions
c. Two different irrational solutions
d. Exactly one rational solution

3. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Please show your work.

f(x) = 3x2
4. Without graphing, find the vertex.
F (x)= 5 (x+ 1/4)^2 + 19
a.(- 1/4,19)
b. (19,1/4)
c. (5,19)
d. (1/4 ,19)
5. Without graphing, find the line of symmetry
F (x) = 8 (x+ 1/2)^2+ 17
x = 17
y = 17
x = 1/2
x = - 1/2

6. Without graphing, find the maximum value.

f(x) = -(x + 1)2 - 8
1
2
0
-8

7. Find the x- and y-intercepts. If no x-intercepts exist, state so.

f(x) = x2 + 13x
X - intercepts (0, -13) and (-13, 0); y-intercept (0,0)
X- intercepts (0, 0) and (-13, 0); y-intercept (0,0)
X-intercepts (0, 0) and (13, 0); y-intercept (0,0)
No x-intercept; y-intercept (0,0)

8. Answer the following question. You will need to use the formula 4.9t2 + v0t = s, where t is the time in seconds, v0 is the initial velocity, and s is the distance in meters.

A rock is dropped from a helicopter at an altitude of 227 meters (s). Approximately how long does it take for the rock to reach the ground?
9. 9. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.

A child's bank contains $2.24 in pennies and nickels. If the number of pennies is 40 less than 3 times the number of nickels, then how many pennies are in the bank?