Quadratic Formula
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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?
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Solution Summary
Quadratic Formula is applied. The expert uses discriminant to determine the equations. Two different rational solutions are provided.
Solution Preview
Please refer to the attached file. Cheers.
1. Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work.
x2 + 4x + 13 = 0
Solution:
x=(-4±√(4^2-4(1)(13) ))/2(1)
=(-4±√(-38))/2
No solution
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
Solution:
D=〖10〗^2-4(1)(19)
=24
Therefore, the equation has two different rational solutions.
3. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function ...
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