To find the zero of the quadratic function [tex]\( f(x) = 4x^2 + 24x + 11 \)[/tex], we need to determine which of the given values makes the function equal zero.
The given candidates are:
- [tex]\( x = -9.25 \)[/tex]
- [tex]\( x = -5.5 \)[/tex]
- [tex]\( x = 0.5 \)[/tex]
- [tex]\( x = 3.25 \)[/tex]
We'll evaluate [tex]\( f(x) \)[/tex] for each of these values and see which one yields [tex]\( f(x) = 0 \)[/tex].
1. For [tex]\( x = -9.25 \)[/tex]:
[tex]\[
f(-9.25) = 4(-9.25)^2 + 24(-9.25) + 11
\][/tex]
Calculate this to see if it equals 0.
2. For [tex]\( x = -5.5 \)[/tex]:
[tex]\[
f(-5.5) = 4(-5.5)^2 + 24(-5.5) + 11
\][/tex]
Calculate this to check if [tex]\( f(-5.5) \)[/tex] equals 0.
3. For [tex]\( x = 0.5 \)[/tex]:
[tex]\[
f(0.5) = 4(0.5)^2 + 24(0.5) + 11
\][/tex]
Calculate to check if it results in 0.
4. For [tex]\( x = 3.25 \)[/tex]:
[tex]\[
f(3.25) = 4(3.25)^2 + 24(3.25) + 11
\][/tex]
Calculate this expression to see if it equals 0.
After checking all these calculations, we find that:
For [tex]\( x = -5.5 \)[/tex]:
[tex]\[
f(-5.5) = 4(-5.5)^2 + 24(-5.5) + 11 = 0
\][/tex]
Therefore, the zero of the quadratic function [tex]\( f(x) = 4x^2 + 24x + 11 \)[/tex] is [tex]\( x = -5.5 \)[/tex].
