Question

Select all of the following that are quadratic functions. x = 3y2 – 6y + 5, y + 3 = –2 x 2+ 5 , y = 2 x 2 – 8 x + 6, y= –7 x – 4, y – 3 x = 4 x 3 – x2 + 9, y = 5 x(x + 9) – 8, y – 2 x 2 = 3 x – 2 x 2 + 4

Answer 1

Quadratic functions are identified by the highest power of the variable being 2. Functions such as x = 3y^2 – 6y + 5, y + 3 = –2 x^2 + 5, y = 2 x^2 – 8 x + 6, and y = 5 x(x + 9) – 8 are quadratic functions.

Step-by-step explanation:

To identify quadratic functions, we look for equations where the highest power of the variable is 2. Quadratic functions are in the form ax2 + bx + c, where a, b, and c are constants and a is not zero.

x = 3y2 – 6y + 5 is a quadratic function in terms of y.

y + 3 = –2 x2 + 5 is a quadratic function in terms of x.

y = 2 x2 – 8 x + 6 is a quadratic function in terms of x.

y = –7 x – 4 is not a quadratic function as it is linear.

y – 3 x = 4 x3 – x2 + 9 is not a quadratic function as the highest power of x is 3.

y = 5 x(x + 9) – 8 is a quadratic function after expanding and yielding a term with x2.

y – 2 x2 = 3 x – 2 x2 + 4 simplifies to y = 3x + 4, which is linear and therefore not a quadratic function.

The equations that are quadratic functions are:

x = 3y2 – 6y + 5

y + 3 = –2 x2 + 5

y = 2 x2 – 8 x + 6

y = 5 x(x + 9) – 8

Answer 2

2. y + 3 = -2x^2 + 5

3. y = 2x^2 - 8x + 6

6. y = 5x (x+9) - 8