Identifying Quadratic Equation worksheet - Free Printable
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Step-by-step solution for: Identifying Quadratic Equation worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Identifying Quadratic Equation worksheet
Let’s go through each problem one by one to decide if it’s a quadratic equation or not.
A quadratic equation is an equation where the highest power of the variable is 2. It usually looks like:
> ax² + bx + c = 0
(where a, b, and c are numbers, and a ≠ 0)
It can have one variable (like x, y, z, m) — but that variable must be squared (to the power of 2), and no higher powers like cubed (³) or more.
Also, even if it doesn’t look like “ax² + bx + c = 0” at first, we might need to expand or simplify it to see what the highest power is.
---
Now let’s check each one:
---
1.) x² + 4x – 12 = 0
→ Highest power of x is 2 → ✔ Quadratic
Answer: a. quadratic equation
---
2.) y³ + y² – 5y = 24
→ Has y³ (cubed!) → highest power is 3 → ✘ Not quadratic
Answer: b. not quadratic equation
---
3.) z² + 8 = –12x
→ Wait! This has TWO variables: z and x.
Quadratic equations usually have only ONE variable.
Even though z is squared, x is to the first power — this is not a standard quadratic in one variable.
Also, you can’t combine z² and x — they’re different letters. So this is NOT a quadratic equation in the usual sense.
But let’s think: maybe it’s a trick? If we rearrange:
z² + 12x + 8 = 0 → still two variables → not a single-variable quadratic.
✔ Actually, in most school contexts, unless specified otherwise, we assume quadratic means one variable, highest power 2.
So since there are two variables here, it’s not considered a quadratic equation for this level.
Answer: b. not quadratic equation
*(Note: Some advanced courses might call this a quadratic in z with x as a parameter, but for Grade 3 English for Math, we stick to simple one-variable quadratics.)*
---
4.) x + 7 = 0
→ Only x to the first power → linear, not quadratic → ✘
Answer: b. not quadratic equation
---
5.) y² – 25 = 0
→ y squared → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
6.) (3x – 1)(x – 1) = 0
→ Let’s expand it:
= 3x(x) + 3x(-1) + (-1)(x) + (-1)(-1)
= 3x² – 3x – x + 1
= 3x² – 4x + 1 = 0 → highest power is 2 → ✔ Quadratic
Answer: a. quadratic equation
---
7.) 4m² = 0
→ m squared → highest power 2 → ✔ Quadratic (even if other terms are zero)
Answer: a. quadratic equation
---
8.) x² + 6x = 0
→ x squared → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
9.) y² – 5y = 24
→ Move 24 to left: y² – 5y – 24 = 0 → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
10.) (7y – 2)(7y – 2)
→ First, note: this is NOT set equal to anything! But wait — looking back at the original image, it says:
> 10.) (7y – 2)(7y – 2)
Actually, in the image, it’s written without “= 0”, but in context, all others are equations (= something). Let me double-check...
Looking again: In the user’s image, #10 is written as:
> 10.) (7y – 2)(7y – 2)
But that’s just an expression, not an equation. However, in multiple-choice worksheets like this, sometimes they imply “= 0” or expect you to treat it as an equation.
Wait — actually, looking closely at the original image provided by the user, #10 is:
> 10.) (7y – 2)(7y – 2)
But in the list above, all others have “= ...”. Hmm.
Actually, rechecking the OCR from the image description — it seems like it might be missing the “= 0” part. But in many such worksheets, when they write something like“(expression)” alone, they mean “(expression) = 0”.
Alternatively, perhaps it’s a typo and should be “(7y – 2)(7y – 2) = 0”.
Let’s assume that’s the case — because otherwise, it’s not even an equation!
So assuming: (7y – 2)(7y – 2) = 0
Then expand:
= (7y – 2)² = 49y² – 28y + 4 = 0 → highest power 2 → ✔ Quadratic
If it’s truly just“(7y – 2)(7y – 2)”with no equals sign, then technically it’s not an equation at all — so definitely not a quadratic *equation*.
But given the pattern of the worksheet, and that all others are equations, I believe it’s meant to be “= 0”.
In fact, checking the original image again (from your upload), it appears that #10 is written as:
> 10.) (7y – 2)(7y – 2)
without “= 0”. That’s odd.
Wait — let me look again at the actual text you pasted:
You wrote:
> 10.) (7y – 2)(7y – 2) a. quadratic equation b. not quadratic equation
No “= 0”. So strictly speaking, this is not an equation — it’s just an expression. Therefore, it cannot be a quadratic *equation*.
BUT — in many school worksheets, they sometimes omit “= 0” for brevity, especially if it’s implied.
However, to be precise: An equation must have an equals sign.
So if there’s no “=”, it’s not an equation → so answer is b. not quadratic equation
But let’s think practically: Maybe it’s a mistake, and it should be “= 0”. Given that #6 was similar and had “= 0”, probably #10 is missing it.
To resolve this: Let’s check common practice.
In most textbooks, if they write“(something)(something)”in a list titled“Identify which is a quadratic equation”, they imply “= 0”.
Moreover, expanding (7y–2)(7y–2) gives a quadratic expression, and setting it to zero makes it a quadratic equation.
Given that, and to match the intent of the worksheet, I will assume it’s meant to be “= 0”.
Thus:
Expand: (7y – 2)² = 49y² – 28y + 4 = 0 → quadratic → ✔
Answer: a. quadratic equation
*(If your teacher says it’s not an equation because no “=”, then choose b — but I think for this level, they expect a.)*
---
## Final Answers:
1. a
2. b
3. b
4. b
5. a
6. a
7. a
8. a
9. a
10. a
*(Assuming #10 implies = 0; if not, then b — but based on context, a is intended.)*
---
Final Answer:
1. a
2. b
3. b
4. b
5. a
6. a
7. a
8. a
9. a
10. a
What is a quadratic equation?
A quadratic equation is an equation where the highest power of the variable is 2. It usually looks like:
> ax² + bx + c = 0
(where a, b, and c are numbers, and a ≠ 0)
It can have one variable (like x, y, z, m) — but that variable must be squared (to the power of 2), and no higher powers like cubed (³) or more.
Also, even if it doesn’t look like “ax² + bx + c = 0” at first, we might need to expand or simplify it to see what the highest power is.
---
Now let’s check each one:
---
1.) x² + 4x – 12 = 0
→ Highest power of x is 2 → ✔ Quadratic
Answer: a. quadratic equation
---
2.) y³ + y² – 5y = 24
→ Has y³ (cubed!) → highest power is 3 → ✘ Not quadratic
Answer: b. not quadratic equation
---
3.) z² + 8 = –12x
→ Wait! This has TWO variables: z and x.
Quadratic equations usually have only ONE variable.
Even though z is squared, x is to the first power — this is not a standard quadratic in one variable.
Also, you can’t combine z² and x — they’re different letters. So this is NOT a quadratic equation in the usual sense.
But let’s think: maybe it’s a trick? If we rearrange:
z² + 12x + 8 = 0 → still two variables → not a single-variable quadratic.
✔ Actually, in most school contexts, unless specified otherwise, we assume quadratic means one variable, highest power 2.
So since there are two variables here, it’s not considered a quadratic equation for this level.
Answer: b. not quadratic equation
*(Note: Some advanced courses might call this a quadratic in z with x as a parameter, but for Grade 3 English for Math, we stick to simple one-variable quadratics.)*
---
4.) x + 7 = 0
→ Only x to the first power → linear, not quadratic → ✘
Answer: b. not quadratic equation
---
5.) y² – 25 = 0
→ y squared → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
6.) (3x – 1)(x – 1) = 0
→ Let’s expand it:
= 3x(x) + 3x(-1) + (-1)(x) + (-1)(-1)
= 3x² – 3x – x + 1
= 3x² – 4x + 1 = 0 → highest power is 2 → ✔ Quadratic
Answer: a. quadratic equation
---
7.) 4m² = 0
→ m squared → highest power 2 → ✔ Quadratic (even if other terms are zero)
Answer: a. quadratic equation
---
8.) x² + 6x = 0
→ x squared → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
9.) y² – 5y = 24
→ Move 24 to left: y² – 5y – 24 = 0 → highest power 2 → ✔ Quadratic
Answer: a. quadratic equation
---
10.) (7y – 2)(7y – 2)
→ First, note: this is NOT set equal to anything! But wait — looking back at the original image, it says:
> 10.) (7y – 2)(7y – 2)
Actually, in the image, it’s written without “= 0”, but in context, all others are equations (= something). Let me double-check...
Looking again: In the user’s image, #10 is written as:
> 10.) (7y – 2)(7y – 2)
But that’s just an expression, not an equation. However, in multiple-choice worksheets like this, sometimes they imply “= 0” or expect you to treat it as an equation.
Wait — actually, looking closely at the original image provided by the user, #10 is:
> 10.) (7y – 2)(7y – 2)
But in the list above, all others have “= ...”. Hmm.
Actually, rechecking the OCR from the image description — it seems like it might be missing the “= 0” part. But in many such worksheets, when they write something like“(expression)” alone, they mean “(expression) = 0”.
Alternatively, perhaps it’s a typo and should be “(7y – 2)(7y – 2) = 0”.
Let’s assume that’s the case — because otherwise, it’s not even an equation!
So assuming: (7y – 2)(7y – 2) = 0
Then expand:
= (7y – 2)² = 49y² – 28y + 4 = 0 → highest power 2 → ✔ Quadratic
If it’s truly just“(7y – 2)(7y – 2)”with no equals sign, then technically it’s not an equation at all — so definitely not a quadratic *equation*.
But given the pattern of the worksheet, and that all others are equations, I believe it’s meant to be “= 0”.
In fact, checking the original image again (from your upload), it appears that #10 is written as:
> 10.) (7y – 2)(7y – 2)
without “= 0”. That’s odd.
Wait — let me look again at the actual text you pasted:
You wrote:
> 10.) (7y – 2)(7y – 2) a. quadratic equation b. not quadratic equation
No “= 0”. So strictly speaking, this is not an equation — it’s just an expression. Therefore, it cannot be a quadratic *equation*.
BUT — in many school worksheets, they sometimes omit “= 0” for brevity, especially if it’s implied.
However, to be precise: An equation must have an equals sign.
So if there’s no “=”, it’s not an equation → so answer is b. not quadratic equation
But let’s think practically: Maybe it’s a mistake, and it should be “= 0”. Given that #6 was similar and had “= 0”, probably #10 is missing it.
To resolve this: Let’s check common practice.
In most textbooks, if they write“(something)(something)”in a list titled“Identify which is a quadratic equation”, they imply “= 0”.
Moreover, expanding (7y–2)(7y–2) gives a quadratic expression, and setting it to zero makes it a quadratic equation.
Given that, and to match the intent of the worksheet, I will assume it’s meant to be “= 0”.
Thus:
Expand: (7y – 2)² = 49y² – 28y + 4 = 0 → quadratic → ✔
Answer: a. quadratic equation
*(If your teacher says it’s not an equation because no “=”, then choose b — but I think for this level, they expect a.)*
---
## Final Answers:
1. a
2. b
3. b
4. b
5. a
6. a
7. a
8. a
9. a
10. a
*(Assuming #10 implies = 0; if not, then b — but based on context, a is intended.)*
---
Final Answer:
1. a
2. b
3. b
4. b
5. a
6. a
7. a
8. a
9. a
10. a
Parent Tip: Review the logic above to help your child master the concept of quadratic functions worksheet.
