options: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
problem_activity: Problem 1
Expand each expression below as a product of two linear binomials and then multiply to write the product in standard form.
a.
$${(x-5)^2}$$
b.
$${(x+4)^2}$$
c.
$${(x-3)^2}$$
d.
$${(2x+1)^2}$$
e.
$${(3x-2)^2}$$
Describe any patterns you notice between the square of the linear binomial and the resulting quadratic trinomial.
Problem 2
Solve the quadratic equation and then sketch a graph of the parabola.
$${y=(x-4)^2}$$
Problem 3
What is the value of
$$c$$
in the equation below such that the quadratic equation is a perfect square trinomial?
$$y=x^2+12x+c$$


correct_option_index: 0