Question

1. which function is not quadratic?

a. $f(x) = x^2 - 4x + 5$
b. $f(x) = x(x + 6)^2$
c. $f(x) = -4(x + 9)^2$
d. $f(x) = -1x^2 - 3$

Explanation:

Step1: Recall quadratic definition

A quadratic function has the form $f(x)=ax^2+bx+c$ ($a
eq0$), highest degree 2.

Step2: Analyze option a

$f(x)=x^2-4x+5$ has degree 2, quadratic.

Step3: Expand option b

First expand $(x+6)^2$:
$(x+6)^2=x^2+12x+36$
Multiply by $x$:
$f(x)=x(x^2+12x+36)=x^3+12x^2+36x$
This has degree 3, not quadratic.

Step4: Analyze option c

Expand $-4(x+9)^2$:
$-4(x^2+18x+81)=-4x^2-72x-324$
Degree 2, quadratic.

Step5: Analyze option d

$f(x)=-x^2-3$ has degree 2, quadratic.

Answer:

b. $f(x) = x(x+6)^2$