PDF) Grade 9 math worksheets | Marjorie Noquera - Academia.edu - Free Printable

Let’s go through each equation one by one and decide if it’s quadratic or not.

A quadratic equation must have a variable (like x or y) raised to the second power — that means squared, like \(x^2\) or \(y^2\). It can also have other terms like linear terms (\(x\), \(y\)) or constants, but the highest power of any variable must be 2. Also, no variables under roots, in exponents, or in denominators.

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1. \(x + 4y = 1\)
→ Only first powers: x and y are both to the power 1.
→ NOT quadratic

2. \(x^2 - y = 7\)
→ Has \(x^2\) → that’s second power!
→ Even though y is only to the first power, the presence of \(x^2\) makes this quadratic.
→ QUADRATIC

3. \(y = -5x^2 + 2\)
→ Clearly has \(x^2\) → second power.
→ QUADRATIC

4. \(y = 2^x + 1\)
→ Here, x is in the exponent — that’s exponential, not quadratic.
→ Quadratic needs variable squared, not variable as exponent.
→ NOT quadratic

5. \(y = 7 - 4x\)
→ Only x to the first power. Linear equation.
→ NOT quadratic

6. \(y = 6 - 9y^2\)
→ Wait — let’s rearrange: bring all terms to one side:
\(9y^2 + y - 6 = 0\) → now we see \(y^2\) → second power!
→ So yes, it’s quadratic in terms of y.
→ QUADRATIC

7. \(80x - 9y = 0\)
→ Both x and y are to the first power. Linear.
→ NOT quadratic

8. \(x = 9\)
→ This is just a constant value for x. No variable with power 2.
→ Actually, you could think of it as \(x + 0y = 9\), still no square.
→ NOT quadratic

9. \(y = \sqrt{4x - 2}\)
→ Square root means the variable is under a radical → equivalent to power 1/2. Not 2.
→ Also, if you try to square both sides, you get \(y^2 = 4x - 2\), which *is* quadratic in y — BUT the original equation is not written as a polynomial. In standard definition, quadratic equations are polynomials of degree 2. Since this involves a square root, it’s not a polynomial → so not quadratic.
→ NOT quadratic

10. \(-x^2 + 4x + 9 = 0\)
→ Has \(x^2\) → definitely quadratic.
→ QUADRATIC

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Now let’s list them clearly:

1. NOT
2. QUADRATIC
3. QUADRATIC
4. NOT
5. NOT
6. QUADRATIC
7. NOT
8. NOT
9. NOT
10. QUADRATIC

Final Answer:
1. NOT
2. QUADRATIC
3. QUADRATIC
4. NOT
5. NOT
6. QUADRATIC
7. NOT
8. NOT
9. NOT
10. QUADRATIC