Question

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Answer 1

`\begin{array} c \boxed{ \bf{Equations} }&\boxed{ \bf{YES \: OR \: NO}} \\ \\ \tt{1. \: \:y = {x}^(2) + 2} & \tt{YES} \\\tt{2. \: \:y = 2x - 10}& \tt{NO} \\ \tt{3. \: \:y = 9 - {2x}^(2)} & \tt{YES} \\ \tt{ 4. \: \:y = {2}^(x) + 2}& \tt{ NO} \\ \tt{5. \: \:y = {3x}^(2) + {x}^(3) + 2}& \tt{NO} \\ \tt{ 6. \: \:y = {2}^(x) + 3x + 2}& \tt{NO} \\ \tt{ 7. \: \:y = {2x}^(2)} & \tt{ YES} \\ \tt{ 8. \: \:y = (x - 2)(x + 4)}& \tt{YES} \\ \tt{9. \: \:0 = (x - 3)(x + 3) + {x}^(2) - y}& \tt{YES} \\ \tt{10. \: \:{3x}^(3) + y - 2x = 0}& \tt{NO}\end{array}`

Explanation:

We know that,

• A function of degree 2 is called a quadratic function.
• For eg :- 3y² - 8y + 5 , x² + 5x -
  `(1)/(2)` etc.

1. y = x² + 2

• Yes, y = x² + 2 is a quadratic function because its degree is 2.

2. y = 2x - 10

• No, y = 2x - 10 is not a quadratic function because it is a linear function.

3. y = 9 - 2x²

• Yes, y = 9 - 2x² is a quadratic function because its degree is 2.

4. y =
`{2}^(x)` + 2

• No, y =
  `{2}^(x)` + 2 is not a quadratic function because it is a exponential function.

5. y = 3x² + x³ + 2

• No, y = 3x² + x³ + 2 is not a quadratic function because it is a cubic function.

6. y =
`{2}^(x)` + 3x + 2

• No, y =
  `{2}^(x)` + 3x + 2 is not a quadratic function because it is a exponential function + a function of one degree.

7. y = 2x²

• Yes, y = 2x² is a quadratic function because its degree is 2.

8. y = (x - 2)(x + 4)

First of all we can solved the function

We using the identity,

(x + a)(x + b) = x² + (a + b)x + ab

(x - 2)(x + 4)

= x² + (-2 + 4)x + (-2)(4)

= x² + 2x - 8

• Yes, y = (x - 2)(x + 4) that is x² + 2x - 8 is a quadratic function because its degree is 2.

9. 0 = (x - 3)(x + 3) + x² - y

First of all we can solved the function

We using the identity,

(a + b)(a - b) = a² - b²

(x - 3)(x + 3) + x² - y

= x² - 3² + x² - y

= x² - 9 + x² - y

= x² + x² - y - 9

= 2x² - y - 9

• Yes, 0 = (x - 3)(x + 3) + x² - y that is 2x²-y-9 is a quadratic function because its degree is 2.

10. 3x³ + y - 2x = 0

• No, 3x³ + y - 2x = 0 is not a quadratic function because it is a cubic function.