Task Sets: Choose equivalent forms to reveal properties - Common Core Math - HS Algebra

Warm-Up: Review What You Know

These problems review skills you have already learned.

Which expression is equivalent to $(2^3)^4$ ?

$2^7$

$2^{12}$

$8^4$

$2^{34}$

Which pair of factors correctly factors $x^2 - 5x + 6$ ?

$(x - 1)(x - 6)$

$(x + 2)(x + 3)$

$(x - 2)(x - 3)$

$(x - 6)(x + 1)$

For the quadratic $f(x) = x^2 - 6x + 8$ , what is the value of $f(0)$ ? (This is the $y$ -intercept.)

Fluency Practice

Apply the procedures directly. Show all steps.

$Table showing the three forms of a quadratic and what each form reveals: standard reveals y-intercept, factored reveals zeros, vertex reveals the vertex and max/min.$

Factor $f(x) = x^2 - 7x + 10$ and find its zeros. Enter the larger zero.

Factor $g(x) = 2x^2 + x - 6$ and find its zeros. Enter the positive zero as a fraction (e.g., 3/2).

Factor $h(x) = -x^2 + 6x - 8$ and find its zeros. Enter the sum of the two zeros.

Complete the square to write $f(x) = x^2 + 6x + 5$ in vertex form. What is the vertex?

$(-3, -4)$

$(3, -4)$

$(-3, 14)$

$(-6, 5)$

Complete the square to write $f(x) = 2x^2 - 12x + 7$ in vertex form $a(x-h)^2 + k$ .
What is the minimum value $k$ ?

An account earns 8% per year, modeled by $A(t) = (1.08)^t$ where $t$ is in years.
Which expression shows the equivalent quarterly growth factor?

$(1.08)^{t/4}$

$(1.02)^{4t}$

$(1.08^{1/4})^{4t}$

$(1.08^4)^{t/4}$

Exercises: Choosing Equivalent Forms to Reveal Properties

Warm-Up: Review What You Know

Fluency Practice