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Do you wish to test your knowledge of graphing and quadratic functions? Try this grade 11 graphing quadratic functions quiz to test your knowledge and understanding. This is a very common topic. So, the basics of quadratic functions and graphs are important to understand. If you know them, it is time to test your knowledge. All the best! Try to get a perfect score on this quiz. You can share the quiz with others too who wish to practice the quadratic functions on graphs.

• 1.

### Which correctly identifies the values of the parameters a, h, and k for the function f(x) = –2(x + 3)^2 + 1

• A.

A = –2, h = 3, k = 1

• B.

A = 2, h = –3, k =–1

• C.

A = –2, h = –3, k = 1

• D.

A = –2, h = –3, k = –1

C. A = –2, h = –3, k = 1
Explanation
The given function is in the form f(x) = a(x - h)^2 + k, where a represents the vertical stretch/compression, h represents the horizontal shift, and k represents the vertical shift. In the given function f(x) = -2(x + 3)^2 + 1, a = -2 represents a vertical compression by a factor of 2, h = -3 represents a horizontal shift to the left by 3 units, and k = 1 represents a vertical shift upward by 1 unit.

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• 2.

### What is the equation of this graph

• A.

Y = –x^2 + 3

• B.

Y = –3x^2

• C.

Y = –(x + 3)^2

• D.

Y = –(x – 3)^2

D. Y = –(x – 3)^2
Explanation
The graph is a downward-facing parabola with the vertex at (3,0). The equation y = -(x - 3)^2 represents a parabola that is reflected vertically and shifted 3 units to the right. This matches the graph shown.

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• 3.

### Which function includes a translation of 3 units left?

• A.

F(x) = (x + 3)^2 + 1

• B.

F(x) = 3x^2 + 1

• C.

F(x) = (x – 3)^2 + 1

• D.

F(x) = (x + 1)^2 – 3

A. F(x) = (x + 3)^2 + 1
Explanation
The function f(x) = (x + 3)^2 + 1 includes a translation of 3 units to the left. This can be seen by the term (x + 3) in the function, which shifts the graph of the function 3 units to the left. The square term ensures that the shift is applied to the entire function. The +1 term does not affect the translation, but rather shifts the graph 1 unit up. Therefore, the correct answer is f(x) = (x + 3)^2 + 1.

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• 4.

### Consider a parabola P that is congruent to y = x^2 and with vertex at (0, 0).  Find the equation of a new parabola that results if P is translated 3 units

• A.

Y = (x + 3)^2 + 4

• B.

Y = (x – 3)^2 + 4

• C.

Y = (x – 4)^2 + 3

• D.

Y = (x – 3)^2 – 4

B. Y = (x – 3)^2 + 4
Explanation
The given equation y = (x - 3)^2 + 4 represents a parabola that has been translated 3 units to the right from the original parabola y = x^2. The term (x - 3)^2 indicates that the vertex of the new parabola is at (3, 0), which is 3 units to the right of the original vertex at (0, 0). The constant term +4 indicates that the new parabola has been shifted upward by 4 units compared to the original parabola. Therefore, the equation y = (x - 3)^2 + 4 represents the equation of the new parabola resulting from the translation.

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• 5.

### The formula for compound interest on \$1000at a given interest rate, r, is shown by the function f(r) = 1000(r + 1)^2.  What are the values of the parameters a, h, and k for f(r)

• A.

A = 1000, h = 1, k = 0

• B.

A = 1000, h = 0, k = 1

• C.

A = 0, h = 1000, k = 1

• D.

A = 1000, h = –1, k = 0

D. A = 1000, h = –1, k = 0
• 6.

### Leila dropped a pebble from a bridge that is 100 meters above the river.  The function h(t) = –5t^2 + 100 describes the height of the pebble, h(t), in meters, t seconds after the pebble is dropped.  Which is the axis of symmetry for the graph of the function?

• A.

X = –5

• B.

X = 0

• C.

X = 5

• D.

X = 100

B. X = 0
Explanation
The axis of symmetry for a quadratic function in the form of h(t) = -5t^2 + 100 is given by the equation x = -b/2a. In this case, a = -5 and b = 0, so the equation becomes x = -0/2(-5), which simplifies to x = 0. Therefore, the axis of symmetry for the graph of the function is x = 0.

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• 7.

### Which equation shows a translation of 3 left and vertical compression by a factor of 2 to the graph y = x^2

• A.

Y = 2(x – 3)^2

• B.

Y = 2(x + 3)^2

• C.

Y = ½(x – 3)^2

• D.

Y = ½(x + 3)^2

D. Y = ½(x + 3)^2
Explanation
The equation y = ½(x + 3)^2 shows a translation of 3 units to the left and a vertical compression by a factor of 2 to the graph y = x^2. The translation of 3 units to the left is represented by the term (x + 3), which shifts the graph horizontally. The vertical compression by a factor of 2 is represented by the coefficient ½, which compresses the graph vertically. Therefore, the given equation satisfies both the translation and compression requirements.

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• 8.

### Joanne hit a ball straight up into the air.  The height of the ball in meters, is given by the function h(t) = –5(t – 3)^2 + 45 t seconds after the ball is hit.  In how many seconds will the ball hit the ground?

• A.

3

• B.

6

• C.

9

• D.

45

B. 6
Explanation
The ball will hit the ground when the height is 0. To find this, we set the function h(t) equal to 0 and solve for t. -5(t - 3)^2 + 45t = 0.
Now, isolate the variable t:
5(t - 3)^2 = 45
(t - 3)^2 = 9
Take the square root of both sides:
t - 3 = ±√9
t - 3 = ±3
Now, solve for t:
t - 3 = 3 t = 3 + 3 t = 6 seconds
t - 3 = -3 t = 3 - 3 t = 0 seconds
Since the ball is hit at t = 0, we only consider positive values of t. Thus, the ball will hit the ground in 6 seconds.

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• 9.

### Kevin threw a ball straight up with an initial speed of 20 metres of second.  The function y = –5(x – 2)^2 + 20 describes the ball’s height, in metres, t seconds after Kevin threw it.  What are the coordinates of the vertex?

• A.

(–5,2)

• B.

(2,20)

• C.

(20,2)

• D.

(–5,20)

B. (2,20)
Explanation
The vertex of a quadratic function in the form y = a(x-h)^2 + k is (h,k). In this case, the function is y = –5(x – 2)^2 + 20, so the vertex is (2, 20).

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• 10.

### Which equation describes a parabola that opens downward, is congruent to y = x^2, and has its vertex at (0, 3)

• A.

Y = (x + 3)^2 – 1

• B.

Y = –x^2 + 3

• C.

Y = –(x – 3)^2

• D.

Y = x^2 + 3

B. Y = –x^2 + 3
Explanation
The equation y = -x^2 + 3 describes a parabola that opens downward because the coefficient of x^2 is negative. The vertex of the parabola is at (0, 3) because the constant term in the equation represents the y-coordinate of the vertex. Additionally, the equation is congruent to y = x^2 because it has the same general form, but with a negative coefficient for x^2.

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• Oct 23, 2023
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• Sep 08, 2009
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