FINDING VERTEX OF A QUADRATIC FUNCTION WORKSHEET

In each case, find the vertex.

Problem 1 :

y = x² - 4x + 5

Problem 2 :

y = x² - 16x + 70

Problem 3 :

y = x² + 4x + 2

Problem 4 :

y = -3x² + 48x - 187

Problem 5 :

y = -2x² - 12x - 12

Problem 6 :

y = 3x² + 18x + 18

Problem 7 :

y = 2x² + 3

Problem 8 :

y = 4x² - 56x + 200

Problem 9 :

y = -8x² - 80x - 199

Problem 10 :

y = -2x² + 20x - 52

Answers

1. Answer :

Comparing y = ax² + bx + c and y = x² - 4x + 5, we get

a = 1  and  b = -4

x-coordinate of the vertex :

x = 2

y-coordinate of the vertex :

Substitute x = 2 into the given quadratic function.

y = 2² - 4(2) + 5

y = 4 - 8 + 5

y = 1

Vertex :

(2, 1)

2. Answer :

Comparing y = ax² + bx + c and y = x² - 16x + 70, we get

a = 1  and  b = -16

x-coordinate of the vertex :

x = 8

y-coordinate of the vertex :

Substitute x = 8 into the given quadratic function.

y = 8² - 16(8) + 70

y = 64 - 128 + 70

y = 6

Vertex :

(8, 6)

3. Answer :

Comparing y = ax² + bx + c and y = x² + 4x + 2, we get

a = 1  and  b = 4

x-coordinate of the vertex :

x = -2

y-coordinate of the vertex :

Substitute x = -2 into the given quadratic function.

y = (-2)² + 4(-2) + 2

y = 4 - 8 + 2

y = -2

Vertex :

(-2, -2)

4. Answer :

Comparing y = ax² + bx + c and y = -3x² + 48x - 187, we get

a = -3  and  b = 48

x-coordinate of the vertex :

x = 8

y-coordinate of the vertex :

Substitute x = 8 into the given quadratic function.

y = -3(8)² + 48(8) - 187

y = -3(64) + 384 - 187

y = -192 + 384 - 187

y = 5

Vertex :

(8, 5)

5. Answer :

Comparing y = ax² + bx + c and y = -2x² - 12x - 12, we get

a = -2  and  b = -12

x-coordinate of the vertex :

x = -3

y-coordinate of the vertex :

Substitute x = -3 into the given quadratic function.

y = -2(-3)² - 12(-3) - 12

y = -2(9) + 36 - 12

y = -18 + 36 - 12

y = 6

Vertex :

(-3, 6)

6. Answer :

Comparing y = ax² + bx + c and y = 3x² + 18x + 18, we get

a = 3  and  b = 18

x-coordinate of the vertex :

x = -3

y-coordinate of the vertex :

Substitute x = -3 into the given quadratic function.

y = 3(-3)² + 18(-3) + 18

y = 3(9) - 54 + 18

y = 27 - 54 + 18

y = -9

Vertex :

(-3, -9)

7. Answer :

Comparing y = ax² + bx + c and y = 2x² + 3, we get

a = 2  and  b = 0

x-coordinate of the vertex :

x = 0

y-coordinate of the vertex :

Substitute x = 0 into the given quadratic function.

y = 2(0)² + 3

y = 3

Vertex :

(0, 3)

8. Answer :

Comparing y = ax² + bx + c and y = 4x² - 56x + 200, we get

a = 4  and  b = -56

x-coordinate of the vertex :

x = 7

y-coordinate of the vertex :

Substitute x = 7 into the given quadratic function.

y = 4(7)² - 56(7) + 200

y = 4(49) - 392 + 200

y = 196 - 392 + 200

y = 4

Vertex :

(7, 4)

9. Answer :

Comparing y = ax² + bx + c and y = -8x² - 80x - 199, we get

a = -8  and  b = -80

x-coordinate of the vertex :

x = -5

y-coordinate of the vertex :

Substitute x = -5 into the given quadratic function.

y = -8(-5)² - 80(-5) - 199

y = -8(25) + 400 - 199 

y = -200 + 400 - 199

y = 1

Vertex :

(7, 1)

10. Answer :

Comparing y = ax² + bx + c and y = -2x² + 20x - 52, we get

a = -2  and  b = 20

x-coordinate of the vertex :

x = 5

y-coordinate of the vertex :

Substitute x = 5 into the given quadratic function.

y = -2(5)² + 20(5) - 52

y = -2(25) + 100 - 52 

y = -50 + 100 - 52

y = -2

Vertex :

(5, -2)

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