Question

The steps to derive the quadratic formula are shown below:

Answer 1

User: Maria Sanchez
In Course: Algebra I V17 ( 3939)
Instructor: Kelly Leger
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09.10 Module Nine Test Part 1

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Question 1 (Multiple Choice Worth 4 points)

[09.06 MC]

A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?

graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37

f(x) because an increasing quadratic function will eventually exceed an increasing exponential function

g(x) because an increasing exponential function will eventually exceed an increasing quadratic function

f(x) because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect

g(x) because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect

Question 2 (Multiple Choice Worth 4 points)

[09.05 MC]

David kicks a soccer ball off the ground and in the air with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

17.9 feet

18.2 feet

18.7 feet

19.1 feet

Question 3 (Multiple Choice Worth 4 points)

[09.04 MC]

Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.

No real solutions

x ≈ -3.27 and x ≈ 0.77

x ≈ -2.98 and x ≈ -7.02

x ≈ -0.77 and x ≈ 3.27

Question 4 (Multiple Choice Worth 4 points)

[09.05 MC]

If 10C = 9Y2 - 3, which equation best represents Y?

Y = square root of 10 times C plus 3 over 9

Y = square root of 10 times C minus 3 over 9

Y = square root of 3 minus 10 times C over 9

Y = square root of 3 plus 10 times C over 9

Question 5 (Multiple Choice Worth 4 points)

[09.01 MC]

Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 4 to x = 6 represent?

The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.

The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.

The water travels an average distance of 5 feet from 4 seconds to 6 seconds.

The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

Question 6 (Multiple Choice Worth 3 points)

[09.01 MC]

A toy rocket was launched from the ground. The function f(x) = -16x2 + 160x shows the height of the rocket f(x), in feet, from the ground at time x seconds.

What is the axis of symmetry of the graph of f(x) and what does it represent?

x = 10; it takes 10 seconds to reach the maximum height and 10 seconds to fall back to the ground

x = 10; it takes 10 seconds to reach the maximum height and 20 seconds to fall back to the ground

x = 5; it takes 5 seconds to reach the maximum height and 10 seconds to fall back to the ground

x = 5; it takes 5 seconds to reach the maximum height and 5 seconds to fall back to the ground

Question 7 (Multiple Choice Worth 4 points)

[09.05 MC]

Emily wants to hang a painting in a gallery but the painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. The frame must have an equal width of x on each side. Which quadratic equation represents the area of the painting and frame combined?

Image of a frame 5 feet wide by 6 feet long, with an of x on the bottom and right sides

4x2 + 22x - 1 = 0

4x2 + 22x + 31 = 0

x2 + 11x - 1 = 0

x2 + 11x + 31 = 0

Question 8 (Multiple Choice Worth 4 points)

[09.04 MC]

The steps to derive the quadratic formula are shown below:

Step 1: ax2 + bx + c = 0
Step 2: x2 + b over ax + c over a = 0
Step 3: x2 + b over a x = - c over a
Step 4: x2 +b over a x + square of quantity of b over 2 times a = -c over a + square of quantity of b over 2 times a
Step 5: x plus b over 2 times a, all squared = -c over a + square of quantity of b over 2 times a
Step 6: x + b over 2 times a = square root of all of negative c over a plus the square of the quantity b over 2 times a
Step 7: x = - b over 2 times a ± square root of all of negative c over a plus the square of the quantity b over 4 times a = -b over 2 times a ± square root of the quantity of b squared minus 4 times a times c over 4 times a squared= negative b plus or minus square root of b squared minus 4 times a times c over 2 times a

Which of the following statements best describes the first incorrect step?

In Step 4, square of quantity of b over 2 times a instead of b over 2 times a was added on both sides.

In Step 5, x plus b over 2 times a, all squared was written instead of x plus b over 4 times a, all squared .

In Step 6, -c over a was written instead of c over a inside the root.

In Step 7, b over 4 times a, all squared was written instead of square of quantity of b over 2 times a inside the root.

Answer 2

what was 8?

Answer 3

yeah what was 8