The Advanced Math Worksheet form is a comprehensive tool designed for students to practice and master concepts related to quadratic equations. It covers a wide range of exercises that require writing quadratic equations in standard form—expressed as \(y = ax^2 + bx + c\)—and identifying the coefficients \(a\), \(b\), and \(c\). This worksheet not only helps students understand the structure of quadratic equations but also guides them in determining the direction in which a parabola opens (upwards or downwards) and whether it has a minimum or maximum value. Moreover, it includes exercises for finding the line of symmetry, a crucial concept that helps in graphing these equations efficiently. It further extends into more advanced territory by asking students to calculate the vertex of the parabola, providing both the coordinates and understanding of its significance in graph representation. Created by Mr. Chvatal, the worksheet serves as a valuable resource for students to practice these concepts, with sample exercises and step-by-step answers that reinforce understanding and ensure students are well-equipped to tackle quadratic equations in their studies.
| Question | Answer |
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| Form Name | Advanced Math Worksheet Form |
| Form Length | 4 pages |
| Fillable? | No |
| Fillable fields | 0 |
| Avg. time to fill out | 1 min |
| Other names | standard form line of symmetry and vertex for quadratic equations answer key, advanced math vertex form to standard form answers, vertex to standard form worksheet, vertex form to standard form worksheet |
Worksheet: Standard form, line of symmetry and vertex for quadratic equations
Name:_______________________________________ |
Date:__________________ |
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Mr. Chvatal |
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Practice writing quadratic equations in standard form and identifying a, b and c. |
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Remember, standard form is y = ax2 + bx + c . |
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Sample #1: |
y = −2 x + x2 − 8 |
Sample #2: |
y = −25 + x2 |
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Answer: |
y = x2 − 2 x − 8 |
Answer: |
y = x2 − 25 |
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a = 1 , b = −2 , c = −8 |
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a = 1 , b = 0 , c = −25 |
1. |
y = x2 + 3x + 11 |
2. |
y = x2 − 7 x − 11 |
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3. |
y = 4 x + x2 − 9 |
4. |
y = 16 − x + 3x2 |
5. |
y = x2 − 9 |
6. |
y = 2 x2 + 5x |
7. |
y = −3 − 4 x2 |
8. |
y = 6 x2 |
9. |
y = − x2 − 8 + 6 x |
10. |
y = x − x2 |
For the following quadratic equations, identify a, b and c, determine whether the parabola opens up or down, and whether there is a minimum or a maximum.
Sample #1: |
y = x2 − 2 x + 7 |
Sample #2: |
y = − x 2 + 8 |
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Answer: |
a = 1 , b = −2 , c = 7 |
Answer: |
a = −1 , b = 0 , c = 8 |
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Opens up; minimum. |
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Opens down; maximum. |
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y = x2 + 3x + 12 |
2. |
y = 2 x 2 − 3x − 1 |
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3. |
y = − x 2 − 12 x + 4 |
4. |
y = x2 + 5x − 9 |
5. |
y = −7 x 2 − 9 x − 3 |
6. |
y = 5x − x2 − 1 |
7. |
y = −9 + 5x2 |
8. |
y = 3x2 |
9. |
y = −10 x2 − 70 + 6 x |
10. |
y = 12 x + 12 x2 |
For the following quadratic equations, identify a, b and c, and then find the equation for the line of symmetry.
Sample #1: |
y = x2 + 6 x − 5 |
Sample #2: |
y = −2 x2 − 5x + 7 |
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Answer: |
a = 1 , b = 6 , c = −5 |
Answer: |
a = −2 , b = −5 , c = 7 |
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The line of symmetry: |
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The line of symmetry: |
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x = |
−(6) |
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x = |
−(−5) |
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2(1) |
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2(−2) |
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x = −3 |
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5 |
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x = − |
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4 |
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1. |
y = x2 + 4 x + 12 |
2. |
y = x2 + 10 x − 3 |
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3. |
y = x2 − 12 x + 4 |
4. |
y = 2 x2 + 8x − 5 |
5. |
y = −3x2 + 6 x − 1 |
6. |
y = − x2 − 2 x − 2 |
7. |
y = x2 + 3x − 8 |
8. |
y = 4 x2 − 16 |
9. |
y = −8x 2 |
10. |
y = 2 x2 − 7 x |
For the following quadratic equations, identify a, b and c, and then find the equation for the line of symmetry, the minimum/maximum, and the coordinates of the vertex.
Sample #1: |
y = x2 − 4 x − 5 |
Sample #2: |
y = − x2 − 8x + 1 |
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Answer: |
a = 1 , b = −4 , c = −5 |
Answer: |
a = −1 , b = −8 , c = 1 |
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The line of symmetry: |
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The line of symmetry: |
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x = |
−(−4) |
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x = |
−(−8) |
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2(1) |
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2(−1) |
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x = 2 |
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x = −4 |
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The minimum: |
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The maximum: |
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y = (2)2 − 4(2) − 5 |
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y = −(−4)2 − 8(−4) + 1 |
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y = −9 |
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y = 17 |
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The vertex: |
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The vertex: |
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(2, −9) |
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(−4,17) |
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1. |
y = x2 − 6 x + 2 |
2. |
y = x2 − 2 x + 7 |
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3. |
y = − x2 − 2 x + 3 |
4. |
y = x 2 − 16 |