DC CAPE Algebra II Interpreting Functions Practice

Interpreting Functions skills

interpret functions that arise in applications in terms of the context

analyze functions using different representations

compare properties of two functions each represented in a different way

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

8 free questions · 0/0 correct

Practice playeasy

For which value of $x$ does the graph of $y = (x - 15)(x + 7)$ intercept the $x$ -axis?

Set $y = 0$ : $(x - 15)(x + 7) = 0$ . The zeros are $x = 15$ and $x = -7$ . Of the choices, $15$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x - 9)^2 - 2$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 1 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 9$ , so the vertex is at $x = 9$ . Therefore, $f(x)$ reaches its minimum when $x = 9$ .

Practice playeasy

The equation $y = x^2 + 4x + 3$ models a quantity $y$ in terms of $x$ . For what value of $x$ is $y$ as small as possible?

The parabola opens upward, so the smallest $y$ is at the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 1$ and $b = 4$ , so $x = -\dfrac{4}{2(1)} = -\dfrac{4}{2} = -2$ . Therefore, $y$ is as small as possible when $x = -2$ .

Practice playeasy

The $x$ -intercept of the graph of $y = 6x + 24$ in the coordinate plane is $(x, 0)$ . What is the value of $x$ ?

At the $x$ -intercept, $y = 0$ , so $0 = 6x + 24$ , $6x = -24$ , and $x = -4\textsf{.}$

Practice playeasy

The graph of $y = -2(x + 15)(x - 8)(x + 3)$ intercepts the $x$ -axis at which value of $x$ ?

Set $y = 0$ : $-2(x + 15)(x - 8)(x + 3) = 0$ . The constant $-2 \neq 0$ , so the zeros are $x = -15$ , $x = 8$ , and $x = -3$ . Among the choices, only $8$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = 3(x - 1)^2 + 7$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 3 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 1$ , so the vertex is at $x = 1$ . The leading coefficient $3$ does not change the $x$ -coordinate of the vertex. Therefore, $f(x)$ reaches its minimum when $x = 1$ .

Practice playmedium

For what value of $x$ does $y = 2x^2 + 12x + 4$ reach a minimum?

The parabola opens upward, so the smallest $y$ is at the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 2$ and $b = 12$ , so $x = -\dfrac{12}{2(2)} = -\dfrac{12}{4} = -3$ . Therefore, $y$ reaches its minimum when $x = -3$ .