# Grade 11 Multiple Transformations To Graph Quiz

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Have you practiced grade 11 multiple transformations to graph well? Take this quiz, give it a try, and see how well you have understood the concepts of multiple transformations to the graph. This quiz will not only test your knowledge but enhance it too. So, you must go for this quiz and practice the math questions about multiple transformations to the graph. All the best for this quiz! You will get a perfect score on this quiz with all the correct answers. Do not forget to share the quiz with others.

Questions and Answers
• 1.

### Functions of the g(x) = a(x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of

• A.

F(x) = 2x

• B.

F(x) = x^2

• C.

F(x) = (x – 1)^2

• D.

F(x) = x + 2

Correct Answer
B. F(x) = x^2
Explanation
The given correct answer, f(x) = x^2, is the original function before any transformations are applied. This can be inferred from the statement "Functions of the g(x) = a(x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of f(x) = x^2." This implies that f(x) = x^2 is the starting point or base function, and g(x) = a(x – h)^2 is a transformed version of f(x).

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• 2.

### List the sequence of steps required to graph the function f(x) = –(x + 4)^2 – 6

• A.

Horizontal translation 4 units to the right, vertical compressions by a factor of 1, vertical translation 6 units down

• B.

Horizontal translation 4 units to the right, reflection in the x-axis, vertical translation 6 units down

• C.

Horizontal translation 4 units to the left, vertical translation 6 units up, reflection in the x–axis

• D.

Horizontal translation 4 units to the left, reflection in x-axis, vertical translation 6 units down

Correct Answer
D. Horizontal translation 4 units to the left, reflection in x-axis, vertical translation 6 units down
Explanation
The correct answer is "Horizontal translation 4 units to the left, reflection in x-axis, vertical translation 6 units down". This is because the function f(x) = –(x + 4)^2 – 6 can be transformed by first translating it 4 units to the left, then reflecting it in the x-axis, and finally translating it 6 units down. This sequence of steps will result in the correct graph of the function.

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• 3.

### Which function matches the graph?

• A.

F(x) = –2(x – 3)^2 + 1

• B.

F(x) = 2(x + 3)^2 – 1

• C.

F(x) = (x + 3)^2 + 2

• D.

F(x) = ½ (x – 3)^2 – 1

Correct Answer
B. F(x) = 2(x + 3)^2 – 1
Explanation
The given function f(x) = 2(x + 3)^2 – 1 matches the graph. This can be determined by analyzing the equation. The function has a parabolic shape with a vertex at (-3, -1) and the coefficient 2 in front of the squared term indicates that the parabola opens upwards. The -1 at the end of the equation shifts the graph one unit downwards. Therefore, this equation corresponds to the given graph.

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• 4.

### Consider a parabola P that is congruent to y = x2, opens upward, and has vertex (–1, 3). Now find the equation of a new parabola that results if p is reflected in the x-axis and translated 3 units down

• A.

Y = –(x + 4)^2 + 3

• B.

Y = (x – 1)^2 + 6

• C.

Y = – (x + 1)^2

• D.

Y = – (x – 2)^2 + 3

Correct Answer
C. Y = – (x + 1)^2
Explanation
The original parabola P is congruent to y = x^2, opens upward, and has vertex (-1, 3). Reflecting the parabola in the x-axis will change the sign of the x-term, resulting in y = -x^2. Translating the parabola 3 units down will change the y-coordinate of the vertex from 3 to 3 - 3 = 0. Therefore, the equation of the new parabola is y = -(x + 1)^2, which matches the given answer.

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• 5.

### A stonewashed jean company has determined the cost in dollars (c) per tonne of stones mined is given by c(x) = 0.2(x – 5)^2 + 7, where x is the number of tonnes of stone. How does the vertex of the parabola of the function compare to the vertex of f(x) = x^2

• A.

Down 5 units and right 7 units

• B.

Up 7 units and left 5 units

• C.

Up 7 units and right 5 units

• D.

Up 5 units and right 7 units

Correct Answer
D. Up 5 units and right 7 units
Explanation
The vertex of the parabola of the function c(x) = 0.2(x – 5)^2 + 7 is obtained by shifting the vertex of the function f(x) = x^2 right by 5 units and up by 7 units. Therefore, the vertex of c(x) is up 5 units and right 7 units compared to the vertex of f(x).

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• 6.

### The graphs of y = x2 and another parabola are shown below. What is a possible equation for the second parabola?

• A.

Y = 2x^2 + 1

• B.

Y = ½ x^2 + 1

• C.

Y = 2(x + 1)^2

• D.

Y = –2x^2 – 1

Correct Answer
A. Y = 2x^2 + 1
Explanation
The graph of y = x^2 is a parabola that opens upwards. The given equation y = 2x^2 + 1 is also a parabola that opens upwards and is shifted vertically upwards by 1 unit compared to y = x^2. Therefore, it is a possible equation for the second parabola.

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• 7.

### (4, 16) is a key point on the graph of f(x) = x2.  If the parabola is translated horizontally, 3 units left and reflected vertically in the x-axis, what are the coordinates of the image of the key point?

• A.

(7, –16)

• B.

(–1, 16)

• C.

(1, –16)

• D.

(–1, –16)

Correct Answer
C. (1, –16)
Explanation
When the parabola is translated horizontally 3 units left, the x-coordinate of the key point (4, 16) will decrease by 3 units to give us (1, 16). Then, when the parabola is reflected vertically in the x-axis, the y-coordinate of the key point will change its sign, resulting in (1, -16). Therefore, the coordinates of the image of the key point are (1, -16).

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• 8.

### Sheila threw a ball into the air. The function h(t) = –5(t – 1)2 + 5 models the height of the ball h(t), in meters, t seconds after the ball is thrown. Which of the following was not a transformation applied to f(x) = x2 to obtain the graph of h(t) = –5(t – 1)2 + 5

• A.

Vertical reflection in the x–axis

• B.

Vertical translation 5 units up

• C.

Horizontal translation 1 unit to the right

• D.

Vertical compression by a factor of 1/5

Correct Answer
D. Vertical compression by a factor of 1/5
Explanation
The graph of h(t) = –5(t – 1)2 + 5 is a vertical compression of the graph of f(x) = x2. This means that the graph of h(t) is narrower and taller than the graph of f(x). The factor of compression is 1/5, which means that the graph of h(t) is compressed vertically by a factor of 1/5 compared to the graph of f(x). Therefore, the correct answer is that a vertical compression by a factor of 1/5 was not applied to f(x) to obtain the graph of h(t).

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• 9.

### The graphs of y = x2 and another parabola are shown below.  What is the first step that should be performed to transform y = x2 to the second parabola?

• A.

Horizontal translation 4 units left

• B.

Vertical translation 3 units up

• C.

Vertical stretch by a factor of 2

• D.

Reflection in x-axis

Correct Answer
C. Vertical stretch by a factor of 2
Explanation
To transform the graph of y = x^2 to the second parabola, the first step that should be performed is a vertical stretch by a factor of 2. This means that every y-coordinate of the original parabola will be multiplied by 2, resulting in a steeper and narrower parabola.

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• 10.

### What would be the coordinates for C'' if C(-1, -4) was rotated 180° to create C', then C' was reflected over the line y=-x?

• A.

(4, 1)

• B.

(1, 4)

• C.

(-4, -1)

• D.

(-1, -4)

Correct Answer
C. (-4, -1)
Explanation
If point C(-1, -4) is rotated 180 degrees around the origin, it will end up at the point C'(1, 4). Then, if C' is reflected over the line y=-x, the x and y coordinates will swap, resulting in the point C''(-4, -1).

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