HSA.SSE.B.3 Tutor Intake — Equivalent Forms and Revealed Properties

The quadratic $f(x) = 2(x-1)(x-3)$ is written in factored form.
What information does this form reveal most directly?

A student needs to find the x-intercepts (zeros) of
$f(x) = x^2 - 6x + 8$. Which equivalent form should the
student produce?

A student needs to find the minimum value of
$g(x) = x^2 + 4x - 1$. Which equivalent form should the
student produce?

Factor $f(x) = x^2 - 5x + 6$ to find its zeros.

The factored form is $(x - 2)(x - p)$ for some value $p$.
What is $p$?

Complete the square to write $f(x) = x^2 + 6x - 2$ in vertex form.

Step 1: $(x^2 + 6x + \square) - \square - 2$
Step 2: $(x + 3)^2 - k$

What is the value of $k$ (the minimum value of the function)?

A savings account earns $12\%$ annually, modeled by $f(t) = (1.12)^t$
where $t$ is in years. To find the equivalent monthly growth factor,
use the identity $(1.12)^t = \bigl((1.12)^{1/12}\bigr)^{12t}$.

Rounded to four decimal places, $(1.12)^{1/12} \approx$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

Enter your answer as a decimal (e.g., $1.0095$).