Q: A ladder leans against a building, making an angle of $$75^ ext{o}$$ with the ground and reaching a point $$9.7$$ meters above the ground. What is the length of the ladder, rounded to the nearest tenth of a meter?

$$9.7 \div \sin 75^\text{o} \approx 10.0$$ meters

Q: Which value of the discriminant $$b^2 - 4ac$ indicates that a quadratic equation has two irrational roots?

$$b^2 - 4ac$$ \u003e 0$$ \text{ and is not a perfect square}

Q: A boy flying a kite lets out $$400$$ feet of string, which makes an angle of $$52^\text{o}$$ with the ground. Assuming the string is straight, how high above the ground is the kite, to the nearest foot?

$$400 \times \sin 52^\text{o} \approx 315$$ feet

Q: A wire attached to the top of a pole reaches a stake in the ground $$20$$ meters from the foot of the pole and makes an angle of $$58^\text{o}$$ with the ground. What is the length of the wire, to the nearest meter?

$$20 \div \cos 58^\text{o} \approx 38$$ meters

Q: From the top of a lighthouse $$190$$ feet high, the angle of depression of a boat out at sea is $$34^\text{o}. $$What is the distance from the boat to the base of the lighthouse, to the nearest foot?

$$190 \div \tan 34^\text{o} \approx 280$$ feet

Q: An airplane rises at an angle of $$14^\text{o}$$ with the ground and covers a horizontal distance of $$1,500$$ feet. What is the length of the airplane's path, to the nearest foot?

$$1,500 \div \cos 14^\text{o} \approx 1,546$$ feet

Q: A wooden beam $$6$$ meters long leans against a wall and makes an angle of $$71^\text{o}$$ with the ground. How high up the wall does the beam reach, to the nearest tenth of a meter?

$$6 \times \sin 71^\text{o} \approx 5.7$$ meters

Question 1

Given the quadratic equation $$y = x^2$ - 2x - 3$$, which of the following statements is TRUE about its graph?

Accepted Answer

The parabola opens upward and has two x-intercepts.

Question 2

For the quadratic equation $$y = -x^2$ - 4x + 5$$, what are the coordinates of the vertex?

Accepted Answer

(-2, 9)

Question 3

A ladder leans against a building, making an angle of $$75^	ext{o}$$ with the ground and reaching a point $$9.7$$ meters above the ground. What is the length of the ladder, rounded to the nearest tenth of a meter?

Accepted Answer

$$9.7 \div \sin 75^	ext{o} \approx 10.0$$ meters

Question 4

Which value of the discriminant $$b^2 - 4ac$ indicates that a quadratic equation has two irrational roots?

Accepted Answer

$$b^2 - 4ac$$ \u003e 0$$ 	ext{ and is not a perfect square}

Question 5

In the equation $$y = ax^2$ + bx + c$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = \frac{-b}{2a}$$

Question 6

A boy flying a kite lets out $$400$$ feet of string, which makes an angle of $$52^	ext{o}$$ with the ground. Assuming the string is straight, how high above the ground is the kite, to the nearest foot?

Accepted Answer

$$400 	imes \sin 52^	ext{o} \approx 315$$ feet

Question 7

Given a right triangle with legs $$a = 3$$, $$b = 4$$, and hypotenuse $$c$$, what is the exact value of $$c$$?

Accepted Answer

$$c = 5$$

Question 8

If $$	an A = \frac{5}{6} in a $$right triangle, what is the exact value of $$\sin A$$?

Accepted Answer

$$\frac{5}{\sqrt{61}}$$

Question 9

For the quadratic equation $$y = x^2$ - 4x + 4$$, what is the number and type of x-intercepts?

Accepted Answer

One rational x-intercept

Question 10

A wire attached to the top of a pole reaches a stake in the ground $$20$$ meters from the foot of the pole and makes an angle of $$58^	ext{o}$$ with the ground. What is the length of the wire, to the nearest meter?

Accepted Answer

$$20 \div \cos 58^	ext{o} \approx 38$$ meters

Question 11

In a $$30^	ext{o}$$-$$60^	ext{o}$$-$$90^	ext{o}$$ triangle, if the side opposite the $$30^	ext{o}$$ angle is $$8$$, what is the length of the hypotenuse?

Accepted Answer

$$16$$

Question 12

From the top of a lighthouse $$190$$ feet high, the angle of depression of a boat out at sea is $$34^	ext{o}. $$What is the distance from the boat to the base of the lighthouse, to the nearest foot?

Accepted Answer

$$190 \div 	an 34^	ext{o} \approx 280$$ feet

Question 13

If the quadratic equation $$y = -x^2$ - 6x - 8 is $$graphed, what is the direction of the parabola and how many x-intercepts does it have?

Accepted Answer

Opens downward, two x-intercepts

Question 14

An airplane rises at an angle of $$14^	ext{o}$$ with the ground and covers a horizontal distance of $$1,500$$ feet. What is the length of the airplane's path, to the nearest foot?

Accepted Answer

$$1,500 \div \cos 14^	ext{o} \approx 1,546$$ feet

Question 15

In a $$45^	ext{o}$$-$$45^	ext{o}$$-$$90^	ext{o}$$ triangle, if each leg is $$7$$, what is the exact length of the hypotenuse?

Accepted Answer

$$7 \sqrt{2}$$

Question 16

Given $$\cos A = \frac{2}{3} in a $$right triangle, what is the exact value of $$\sin A$$?

Accepted Answer

$$\frac{\sqrt{5}}{3}$$

Question 17

If the quadratic equation $$y = -x^2$ - 4x - 5 is $$graphed, what is the number and type of x-intercepts?

Accepted Answer

No x-intercepts

Question 18

A wooden beam $$6$$ meters long leans against a wall and makes an angle of $$71^	ext{o}$$ with the ground. How high up the wall does the beam reach, to the nearest tenth of a meter?

Accepted Answer

$$6 	imes \sin 71^	ext{o} \approx 5.7$$ meters

Question 19

For the quadratic equation $$y = 2x^2$ - 8x + 6$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = 2$$

Study Guide: Quadratic Functions, Parabolas, and Right Triangle Trigonometry

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