Question

Select all of the following functions that are quadratic.

a. y=2x²
b. 3=2x²-8
c. y=-2+2x-8
d. y+3x=2x²-8
e. y+3x²=2x+3x²-8

Answer 1

The quadratic functions from the given list are a, b, and d, as they include the x² term and follow the form y = ax² + bx + c with a nonzero.

Step-by-step explanation:

The student asked to select all quadratic functions from a list. A quadratic function is typically of the form y = ax² + bx + c, where a, b, and c are constants, and a ≠ 0. Quadratic functions are also known as second-order polynomials.

From the given functions, let's analyze them one by one:

• a. y=2x²: This is a quadratic function because it has the x² term.
• b. 3=2x²-8: Rearranging this equation gives us y = 2x² - 11, which is also a quadratic function.
• c. y=-2+2x-8: This function lacks the x² term, so it is not a quadratic function; it is linear.
• d. y+3x=2x²-8: Rearranging this gives us y = 2x² - 3x - 8, which is a quadratic function.
• e. y+3x²=2x+3x²-8: Simplifying, we get y = 2x - 8, which is not a quadratic function; it is linear because the 3x² terms cancel each other out.

Therefore, the quadratic functions from the given list are a, b, and d.