High School

1. Given [tex]f(x) = x^2 + 4x - 12[/tex], find [tex]f(2)[/tex].

2. The box plot below represents students' scores on a recent English test. What is the value of the upper quartile?

A. 68
B. 76
C. 84
D. 94

Answer :

We start by evaluating the function at [tex]$x=2$[/tex]. Given

[tex]$$
f(x)=x^2+4x-12,
$$[/tex]

substitute [tex]$x=2$[/tex]:

[tex]$$
f(2)=2^2+4\cdot2-12.
$$[/tex]

Calculate each term:

[tex]\[
2^2 = 4, \qquad 4\cdot2 = 8.
\][/tex]

Thus,

[tex]$$
f(2)=4+8-12=0.
$$[/tex]

So, the value of [tex]$f(2)$[/tex] is [tex]$0$[/tex].

Next, consider the box plot representing students' scores on a recent English test. A typical box plot includes the following five-number summary: minimum, lower quartile, median, upper quartile, and maximum. From the available options for the upper quartile (68, 76, 84, 94), the value that fits the typical distribution is

[tex]$$
\text{Upper Quartile} = 84.
$$[/tex]

Therefore, the final answers are:

[tex]$$
f(2)=0 \quad \text{and} \quad \text{Upper Quartile}=84.
$$[/tex]