algebra 2a - unit 2: key features and graphing quadratics lesson 5-8

what are the coordinates for the vertex of the parabola represented by the quadratic equation y = 2(x + 5)^2 − 6?

(-5, -6)

what are the coordinates of the vertex of the following function? f(x) = x^2 + 10x + 19

(-5, -6)

what are the coordinates of the vertex of the following function? f(x) = x^2 − 14x + 51

(7, 2)

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236017 what is the domain and range of the function represented by the graph?

domain: (−∞, ∞) range: [-16, ∞).

which statement correctly describes the end behavior of the function f(x) = −x^2 − 2x − 6?

as x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches −∞.

the product of a number and 3 more than twice that number is at most 152 which quadratic equation represents the product, where nn represents the smaller integer?

n(2n + 3) ≤ 152

the product of two positive consecutive integers is 72 which quadratic equation represents the product, where n represents the smaller integer?

n(n + 1) = 72

examine the table, which contains some points of a quadratic function. x: 1, 2, 3, 4, 5 f(x): 18, 20, 20, 18, 14 which statements are true about the function? select all that apply.

the function has a maximum. a reasonable estimate of the maximum is 20.25

examine the table, which contains some points of a quadratic function. x: 1, 2, 3, 4, 5 f(x): 20, 20, 18, 14 8 which statements are true about the function? select all that apply.

the function has a maximum. the maximum is greater than 20

examine the graph. https://cdstools.flipswitch.com/asset/media/1236035 which statement is true about the function represented by the graph?

the function has a minimum of 1

examine the graph. https://cdstools.flipswitch.com/asset/media/1236063 which statement is true about the end behavior of the function represented by the graph?

as x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches −∞.

examine the table, which contains some points of a quadratic function. x: -1, 0, 1, 2, 3 f(x): 12, 15, 16, 15, 12 which statement correctly describes the end behavior of the function?

as x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches −∞.

examine the table, which contains some points of a quadratic function. which statement correctly describes the end behavior of the function?

as x approaches −∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞.

which statement correctly describes the end behavior of the function f(x) = x^2 − 2x + 8?

as x approaches −∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞.

examine the graph. https://cdstools.flipswitch.com/asset/media/1236060 what is the domain and range of the function represented by the graph?

domain: (−∞, ∞) range: [−9, ∞)

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236561 which function rule correctly describes the function represented in the graph?

f(x) = -(x + 5)(x - 3)

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236555 which function rule correctly describes the function represented in the graph?

f(x) = -x^2 - 8x - 12

use the quadratic function f(x) = x^2 − 2x −3 to answer the questions. a: what are the zeros of the quadratic function? b: what are the x-intercepts of the function?

a: x = -1 and x = 3 b: (-1, 0) and (3, 0)

examine the graph. https://cdstools.flipswitch.com/asset/media/1236034 which statement is true about the function represented by the graph?

the function has a maximum of 16

examine the graph. https://cdstools.flipswitch.com/asset/media/1236036 which statement is true about the end behavior of the function represented by the graph?

as x approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches infinity.

examine the graph. https://cdstools.flipswitch.com/asset/media/1236062 which statement is true about the function represented by the graph?

the function has a maximum of 25

lesson 8

quadratic equations in context

which graph has the most appropriate labels and scales to graph the function?

https://cdstools.flipswitch.com/asset/media/1236884

examine the table, which contains some points of a quadratic function. which statement is true about the function?

the function has a minimum of -5.

examine the graph. https://cdstools.flipswitch.com/asset/media/1236039 which statements are true about the function represented by the graph? select all that apply.

x = 5 is a zero of the function x = -3 is a zero of the function the range of the function is [−16, ∞).

what is the vertex form of the quadratic function f(x) = x^2 + 4x − 2?

y = (x + 2)^2 - 6

what is the vertex form of the quadratic equation y = −2x^2 + 16x − 24?

y = -2(x - 4)^2 + 8

examine the following description of a function. f(x) = −(x + 7)^2 − 2, where −∞ < x < ∞ which expression correctly describes the range?

−∞ < f(x) ≤ −2

which statements are true about the function f(x) = x^2 − 3x + 2?

the function has a y-intercept at (0, 2) the function has x-intercepts at (1, 0) and (2, 0) as x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞.

examine the table, which contains some points of a quadratic function. which statements are true about the intercepts of the function? select all that apply.

the function has a y-intercept of (0, 8). the function has an x-intercept of (2, 0). the function has an x-intercept of (4, 0).

examine the table, which contains some points of a quadratic function. x: -4, -3, -2, 1, 0 f(x): -2, 0, 0, -2, -6 which statements are true about the intercepts of the function? select all that apply.

the function has an x-intercept of (−3, 0). the function has an x-intercept of (−2, 0). the function has a y-intercept of (0, −6).

what is the maximum or minimum of the following function? f(x) = −(x + 3)^2 − 7

the maximum is -7

lesson 5

key features from graphs: quadratics

what is the maximum or minimum of the following function? f(x) = (x − 4)^2 + 5

the minimum is 5

danice is designing a mat with an 8 * 10 opening for a photo she is going to frame. she wants the mat to have the same width on all four sides, as shown in the figure. the combined area of the photo and the mat will be 24 square inches. which equation represents the combined area of the photo and the mat?

(8 + 2w)(10 + 2w) = 224

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236019 which answers are factors of the function represented by the graph? select all that apply.

(x + 4) (x - 6)

examine the graph. https://cdstools.flipswitch.com/asset/media/1236038 which answers are factors of the function represented by the graph? select all that apply.

(x - 4) (x + 2)

how long does it take the rock to reach 25 feet on its way up?

1 second

if h represents height in feet, and t represents time in seconds, approximately how high is the ball 1.5 seconds after it is thrown?

18.05 feet

examine the following description of a function. f(x) = (x − 1)^2 + 2, where −∞ < x < ∞ which expression correctly describes the range?

2 ≤ f(x) < ∞

the equation that represents the combined area of the photo and the mat is (8 + 2w)(10 + 2w) = 224. what is the width of the mat?

3

the product of two positive, consecutive integers is 72. this can be represented by the following equation, where n represents the smaller number. n(n + 1) = 72 what are the positive, consecutive integers?

8, 9

match each function to the graph that it represents.

f(x) = x^2 + 12x + 33 : https://cdstools.flipswitch.com/asset/media/1236546 g(x) = x^2 + 12x + 38 : https://cdstools.flipswitch.com/asset/media/1236547 h(x) = -2x^2 + 32x - 130 : https://cdstools.flipswitch.com/asset/media/1236548

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236556 which function rule correctly describes the function represented in the graph?

f(x) = x^2 + 8x + 13

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236566 which function rule correctly describes the function represented in the graph?

f(x) = x^2 - 6x + 5

the height of an object that is projected can be modeled using the formula h = −16t^2 + v_0 t + h_0, where hh is the height of the object in feet, tt is the number of seconds from when the object is projected, v_ is the initial speed in feet per second, and h_0 is the initial height in feet. which equation models a rock that is thrown upward from an elevation of 6 feet at a speed of 35 feet per second?

h = -16t^2 + 35t + 6

emanuel can throw a baseball 22 miles per hour. he throws the ball straight up in the air, releasing it at 5.6 feet above the ground. which equation represents the approximate height of the ball during the seconds after it is thrown?

h ≈ −16t^2 + 32.3t + 5.6

examine the table, which contains some points of a quadratic function. x: 2, 3, 4, 5, 6 f(x): 7, 2, -1, -2, -1 which graph represents the same function?

https://cdstools.flipswitch.com/asset/media/1236326

which graphs have a maximum of 6? select all that apply.

https://cdstools.flipswitch.com/asset/media/1236330 https://cdstools.flipswitch.com/asset/media/1236331

examine the table, which contains intercepts of a quadratic function. x: -1, 0, 5 f(x): 0, -5, 0 which graph represents the same function?

https://cdstools.flipswitch.com/asset/media/1236335

which graph matches the following description? the function is decreasing over the interval (−∞, −1) and increasing over the interval (−1, ∞).

https://cdstools.flipswitch.com/asset/media/1236341

examine the table, which contains some points of a quadratic function. x: -3, -2, -1, 0, 1 f(x): -5, -2, -1, -2, -5 which graph represents the same function?

https://cdstools.flipswitch.com/asset/media/1236403

which graph matches the following description? - the function is decreasing over the interval (−∞,3) and increasing over the interval (3, ∞). - the function has a minimum of −2. - the function has a y-intercept of (0, 7).

https://cdstools.flipswitch.com/asset/media/1236407

match each parabola with the equation it represents.

https://cdstools.flipswitch.com/asset/media/1236551 : y = 1/4(x + 1)^2 - 4 https://cdstools.flipswitch.com/asset/media/1236552 : y = -(x - 1)^2 + 4 https://cdstools.flipswitch.com/asset/media/1236553 : y = 2(x - 3)^2 https://cdstools.flipswitch.com/asset/media/1236554 : y = -1/2(x - 4)^2 -1

select the graph that matches the following description. - the function has a maximum of 25 - it is increasing over the interval (−∞, −1) and decreasing over the interval (−1, ∞) - it has x-intercepts at (−6, 0) and (4, 0), and a y-intercept at (0, 24)

https://cdstools.flipswitch.com/asset/media/1236557

which graph represents the same function as the following rule? f(x) = −x^2 − 2x + 24

https://cdstools.flipswitch.com/asset/media/1236562

select the graph that matches the following description. - the function has a minimum of −9 - it is decreasing over the interval (−∞, 2) and increasing over the interval (2, ∞) - it has x-intercepts at (−1, 0) and (5, 0), and a y-intercept at (0, −5).

https://cdstools.flipswitch.com/asset/media/1236567

lesson 7

key features from rules: quadratics

lesson 6

key features from tables: quadratics

which inequality represents all possible values of n?

n ≤ 8

examine the table, which contains some points of a quadratic function. which statements are true about the function? select all that apply.

the function has a minimum. a reasonable estimate of the minimum is −12.25.

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236015 which statements are true about the function represented by the graph? select all that apply.

the function has the x-intercept of (-2, 0) the function has the y-intercept of (0, -8) the function has the x-intercept of (4, 0)

examine the graph. https://cdstools.flipswitch.com/asset/media/1236064 which statements are true about the function represented by the graph? select all that apply.

the function increases between −1 and ∞. the function decreases between −∞ and −1.

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236037 which statements are true about the function represented by the graph? select all that apply.

the function increases over the interval (0, ∞) the function decreases over the interval (−∞, 0)

examine the following quadratic function. f(x) = x^2 −8x + 25 which statement is true about the function?

the function is decreasing over the interval (−∞, 4) and increasing over the interval (4, ∞).

examine the table, which contains some points of a quadratic function. x: 2, 3, 4, 5, 6 f(x): 10, 5, 2, 1, 2 which statement is true about the function?

the function is decreasing over the interval (−∞, 5) and increasing over the interval (5, ∞).

examine the following quadratic function. f(x) = −x^2 + 22x − 114 which statement is true about the function?

the function is increasing over the interval (−∞, 7) and decreasing over the interval (7, ∞)

examine the table, which contains some points of a quadratic function. x: -4, -3, -2, -1, 0 f(x): -3, 0, 1, 0, -3 which statement is true about the function?

the function is increasing over the interval (−∞, −2) and decreasing over the interval (−2, ∞).

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236018 which statements are true about the function represented by the graph? select all that apply.

the function is negative over the interval (-4, 4) the function is positive over the interval (4, ∞) the function is positive over the interval (−∞, -4)

examine the graph. https://cdstools.flipswitch.com/asset/media/1236061 which statements are true about the function represented by the graph? select all that apply.

the function is positive over the interval (3, ∞) the function is negative over the interval (−5, 3) the function is positive over the interval (−∞, −5).

what does the vertex of (1, 21.9) mean in the context of the situation? select all that apply.

the maximum height of the baseball is 21.9 feet. the baseball reaches its maximum height 1 second after it's thrown.

what are the x- and y-intercepts of the function f(x) = −x^2 + 4x − 4?

the point (2, 0) is an x-intercept of the function the point (0, -4) is a y-intercept of the function

what are the x- and y-intercepts of the function f(x) = x^2 − x − 20?

the point (5, 0) is an x-intercept of the function. the point (0, −20) is a y-intercept of the function. the point (−4, 0) is an x-intercept of the function.

what does the range of the function tell you about the situation?

the range of the function contains integers that are greater than or equal to 0, so the product will never be negative.

what does the x-intercept (2.4, 0) represent in this situation?

the rock lands on the ground 2.4 seconds after it is thrown.

examine the following graph. https://cdstools.flipswitch.com/asset/media/1236016 which statements are true about the function represented by the graph? select all that apply.

x = -4 is a zero of the function x = 6 is a zero of the function the domain of the function (−∞, ∞). the range of the function is (−∞, 25]