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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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### James

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get 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. from EN Bilgi.

## analytic geometry Quadratic Functions: Factored Form Assignment

5.0 62 Reviews

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

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

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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).

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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

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  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

dem82 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

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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Lyrx  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

## 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

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James 14 day ago

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