Which of the following equations belongs to the quadratic function family?(1 point)

Question

Responses

y=2(x+1.5)^2−55
y equals 2 left parenthesis x plus 1.5 right parenthesis squared minus 55

y=1.2(2)^x−8
y equals 1.2 left parenthesis 2 right parenthesis superscript x baseline minus 8

y=7.2x−15
y equals 7.2 x minus 15

y=7(x+3.5)^1/2

Answer 1

The equation that belongs to the quadratic function family is:

y = 2(x + 1.5)² - 55

This equation is in the form \( y = a(x - h)^2 + k \), which is the standard form of a quadratic function where \( a \) is a coefficient, and \( (h, k) \) is the vertex of the parabola.

The other equations do not fit this form:

• \( y = 1.2(2)^x - 8 \) is an exponential function.
• \( y = 7.2x - 15 \) is a linear function.
• \( y = 7(x + 3.5)^{1/2} \) involves a square root, which does not represent a quadratic function.

Thus, the correct answer is the first equation.