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    explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

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    analytic geometry Quadratic Functions: Factored Form Assignment Flashcards

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    analytic geometry Quadratic Functions: Factored Form Assignment

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    Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)?

    (-4, 0) (-2, 0) (0, 2) (4, -2)

    Click card to see definition 👆

    B (-2, 0)

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    The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply.

    The vertex is the maximum value.

    The axis of symmetry is x = -4.

    The domain is all real numbers.

    The function is increasing over (-∞, -4).

    The function is negative over (-6, -2).

    Click card to see definition 👆

    B The axis of symmetry is x = -4.

    C The domain is all real numbers.

    E The domain is all real numbers.

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    1/10 Created by Devyn_Bates edgenuity

    Terms in this set (10)

    Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)?

    (-4, 0) (-2, 0) (0, 2) (4, -2) B (-2, 0)

    The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply.

    The vertex is the maximum value.

    The axis of symmetry is x = -4.

    The domain is all real numbers.

    The function is increasing over (-∞, -4).

    The function is negative over (-6, -2).

    B The axis of symmetry is x = -4.

    C The domain is all real numbers.

    E The domain is all real numbers.

    The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function.

    The vertex is the .

    The function is positive

    .

    The function is decreasing

    .

    The domain of the function is

    .

    The range of the function is

    . 1.) maximum value

    2.) for no values of x

    3,) when x > -1

    4.) all real numbers

    5.) all numbers less than or equal to 0

    Graph the function f(x) = (x + 1)(x - 5). Use the drop-down menus to complete the steps needed to graph the function.

    Identify the x-intercepts: (-1, 0) and (5, 0)

    Find the midpoint between the intercepts: (2, 0)

    Find the vertex:

    Find the y-intercept:

    Plot another point, then draw the graph.

    (2,-9) (0,-5)

    What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)?

    (,) (5,-9)

    Which graph represents the function f(x) = (x - 3)2?

    graph C

    Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student's claim is below.

    Jeremiah: The y-intercept is at (15, 0).

    Lindsay: The x-intercepts are at (-3, 0) and (5, 0).

    Stephen: The vertex is at (-4, -1).

    Alexis: The midpoint between the x-intercepts is at (4, 0).

    Which student's claim about the function is correct?

    The claim by is correct. Stephen

    Which function has a vertex at (2, -9)?

    f(x) = -(x - 3)2 f(x) = (x + 8)2

    f(x) = (x - 5)(x + 1)

    f(x) = -(x - 1)(x - 5)

    C f(x) = (x - 5)(x + 1)

    Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions?

    They have the same vertex.

    They have one x-intercept that is the same.

    They have the same y-intercept.

    They have the same range.

    C They have the same y-intercept.

    Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

    sample response :

    The vertex is on the axis of symmetry, so the axis of symmetry is x = 3. Find any two x-intercepts that have the equivalent distance from the axis of symmetry. Use those x-intercepts to write factors of the function by subtracting their values from x. For example, 2 and 4 are each 1 unit from x = 3, so f(x) = (x - 2)(x - 4) is a possible function.

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    Verified questions

    CALCULUS

    Find direction numbers for the line of intersection of the planes x+y+z=1 and x+z=0

    Verified answer CALCULUS

    Billy-Sean O’Hagan is the treasurer at his college fraternity, which recently earned $12,400 in its annual carwash fundraiser. Billy-Sean decided to invest all the proceeds in the purchase of three computer stocks: HAL, POM, and WELL.$ $$ \begin{matrix} & \text{Price per Share} & \text{Dividend Yield}\\ \text{HAL} & \text{\$100} & \text{0.5\\%}\\ \text{POM} & \text{\$20} & \text{1.50\\%}\\ \text{WELL} & \text{\$25} & \text{0\\%}\\ \end{matrix} $$ $If the investment was expected to earn$56 in annual dividends, and he purchased a total of 200 shares, how many shares of each stock did he purchase?

    Source : quizlet.com

    Explain how you could write a quadratic function in factored form that would have a vertex with an x

    Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice) Vertex form of a quadratic equation: (h,k) is vertex

    devlian [24] 1 year ago 14

    Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

    tinct roots. Mathematics 2 answers:

    dem82 [27]1 year ago

    7 0

    Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)

    Vertex form of a quadratic equation: (h,k) is vertex

    y = a(x-h)^2 + k

    The x of the vertex needs to equal 3

    y = a(x-3)^2 + k

    In order to have two distinct roots the parabola must be (+a) upward facing with vertex below the x-axis or (-a) downward facing with vertex above the x-axis. Parabolas are symmetrical so for an easy factorable equation make "a" 1 or -1 depending on if you want the upward/downward facing one.

    y = (x-3)^2 - 1

    Vertex (3,-1) upwards facing with two distinct roots 4 and 2

    y = x^2 -6x + 9 - 1 y = x^2 -6x + 8 y = (x - 4)(x - 2) adrean green 8 months ago

    thanks. that a good answer

    lorasvet [3.4K]1 year ago

    6 0

    The vertex lies on the axis of symmetry, so the axis of symmetry is x = 3. Find any two x-intercepts that are equal distance from the axis of symmetry. Use those x-intercepts to write factors of the function by subtracting their values from x. For example, 2 and 4 are each 1 unit from x = 3, so f(x) = (x – 2)(x – 4) is a possible function.

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    Someone please help me with this question !!!!

    Lyrx [107] Answer: 34.3 in, 36.3 in

    Step-by-step explanation:

    From the question given above, the following data were obtained:

    Hypothenus = 50 in 1st leg (L₁) = L

    2nd leg (L₂) = 2 + L

    Thus, we can obtain the value of L by using the pythagoras theory as follow:

    Hypo² = L₁² + L₂² 50² = L² + (2 + L)²

    2500 = L² + 4 + 4L + L²

    2500 = 2L² + 4L + 4 Rearrange

    2L² + 4L + 4 – 2500 = 0

    2L² + 4L – 2496 = 0

    Coefficient of L² (a) = 2

    Coefficient of L (n) = 4

    Constant (c) = –2496

    L = –b ± √(b² – 4ac) / 2a

    L = –4 ± √(4² – 4 × 2 × –2496) / 2 × 2

    L = –4 ± √(16 + 19968) / 4

    L = –4 ± √(19984) / 4

    L = –4 ± 141.36 / 4

    L = –4 + 141.36 / 4 or –4 – 141.36 / 4

    L = 137.36/ 4 or –145.36 / 4

    L = 34.3 or –36.3

    Since measurement can not be negative, the value of L is 34.3 in

    Finally, we shall determine the lengths of the legs of the right triangle. This is illustrated below:

    1st leg (L₁) = L L = 34.4

    1st leg (L₁) = 34.3 in

    2nd leg (L₂) = 2 + L

    L = 34.4

    2nd leg (L₂) = 2 + 34.3

    2nd leg (L₂) = 36.3 in

    Therefore, the lengths of the legs of the right triangle are 34.3 in, 36.3 in

    5 0 1 year ago

    Source : answer-ya.com

    vertex with an x

    vertex with an x-coordinate of 3 and two distinct roots. have a vertex with an x-coordinate of 3 ... x- x- coordinate of 3 and two distinct roots.

    vertex with an x-coordinate of 3 and two distinct roots.

    vertex with an x-coordinate of 3 and two distinct roots. 1 Answer

    Source : question.ma4p.com

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    James 14 day ago
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