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Quadratic Equation Problem Set

See attached file for full problem description.

4.
a) Solve 36x2 + 49 = 0
b) Find the x-intercept of f(x) = 36x2 + 49

6.
Solve 3x2 - 7 = 0

16.
Solve (t - 2)2 = 25

56.
Use the hang-time function V(T) = 48T2, relating vertical leap to hang time. Tracy McGrady, of the Houston Rockets, has a vertical leap of 40in. What is his hang-time?

18.
a) Solve 49x2 - 14x + 1 = 0
b) Find the x-intercept of f(x) = 49x2 - 14x + 1

22.
Solve 11(x - 2) + (x - 5) = (x + 2) (x - 6)

30.
see attachment

34.
Solve (x + 3)2 + (x - 1)2 = 0

For the following word problems, define the variable(s) and solve.

10. The outside of a picture frame measures 14in. by 20in.; 160in2 of picture shows. Find the width of the frame.

20. The hypotenuse of a right triangle is 22m long. The length of one leg is 10 m less than the other. Find the lengths of the legs.

26. A turbo-jet flies 50mph faster than a super-prop plane. If a turbo-jet goes 200mi in 3hr less time that it takes the super-prop plane to go 2800mi, find the speed of each plane.

38.
Solve for c: a2 + b2 + c2 = d2 (Pythagorean formula in three dimensions)

Attachments

Solution Preview

11.1

4. Solve:

a) 36x2 + 49 = 0

36x2 + 49 = 0
36x2 = - 49
x2 = - 49/36

You can't take the square root of a negative number (unless you include imaginary numbers as solutions). Therefore, there is no solution to the equation 36x2 + 49 = 0.

b) Find the x-intercept of f(x) = 36x2 + 49

The x-intercept would occur when f(x) = 0. This makes this problem exactly the same as part a. There is no x-intercept for this equation.

It looks like a parabola opening up, with its vertex above the x-axis.

Solve. Give the exact solution and approximate solutions to three decimal places, when appropriate.

6. 3x2 - 7 = 0

3x2 - 7 = 0
3x2 = 7
x2 = 7/3
x = ±√(7/3)
x = - 1.528 or 1.528

16. (t - 2)2 = 25

(t - 2)2 = 25
t - 2 = ±√25
t - 2 = - 5 or 5
t = -3 or 7

56. Use the hang-time function V(T) = 48T2, relating vertical leap to hang time.

56. Tracy McGrady, of the Houston Rockets, has a vertical leap of 40in. What is his hang-time?

V(T) = 48T2

40 = 48T2
40/48 = T2
5/6 = T2
T = ±√(5/6)
T = -0.913 or 0.913

T is measured in seconds, so it has to be positive. The answer is T = 0.913 seconds.

18.

a) Solve: 49x2 - 14x + 1 = 0

49x2 - 14x + 1 = 0

We can use the quadratic formula to solve for x:

x = 14 ± √[(14)2 - (4)(49)(1)]
2(49)

x = 14 ± √[196 - 196]
98

x = 14/98 = 0.143

b) Find the x-intercept of f(x) = 49x2 - 14x + 1

The x-intercept would ...

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