In today's blog post, we're going to take a look at an advanced math worksheet form. This worksheet is designed for students who are studying calculus or other higher-level math courses. If you're looking for something to challenge your students, this is the perfect resource! We'll go over how to use the form, and provide a few examples so you can see how it works. Stay tuned for more great math resources from our team!
| 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. |
1. |
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 |