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GenaCL600 [577]
2 years ago
12

Which best describes the transformation that occurs from the graph of f(x)=x^2 to g(x)=(x-2)^2+3?? ​

Mathematics
1 answer:
Leokris [45]2 years ago
3 0

answer right 2, up 3

any function with the following form is a transformation from f(x) = x²

g(x) = (x – a)² + b

were a moves the function to the right when a is a positive number and to the left when its a negative number, and b moves the function up when b is positive and down when its negative.

then for a=2 positive and b=3 positive, we have

right 2, up 3

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vlabodo [156]

Explanation:

Conversion of a quadratic equation from standard form to vertex form is done by completing the square method.

Assume the quadratic equation to be \mathbf{ax^{2}+bx+c=0} where x is the variable.

Completing the square method is as follows:

  1. send the constant term to other side of equal                 \mathbf{ax^{2}+bx=-c}
  2. divide the whole equation be coefficient of \mathbf{x^{2}}, this will give     \mathbf{x^{2}+\frac{b}{a}x=- \frac{c}{a}}
  3. add \mathbf{(\frac{b}{2a})^{2}} to both side of equality                                   \mathbf{x^{2}+2\times\frac{b}{2a}x+\frac{b}{2a}^{2}=-\frac{c}{a}+\frac{b}{2a}^{2}}
  4. Make one fraction on the right side and compress the expression on the left side                                                                          \mathbf{(x+\frac{b}{2a})^{2}=\frac{b^{2}-4ac}{4a^{2}}}
  5. rearrange the terms will give the vertex form of standard quadratic equation                                                                 \mathbf{a(x+\frac{b}{2a})^{2}-\frac{b^{2}-4ac}{4a}=0}

Follow the above procedure will give the vertex form.

(NOTE : you must know that \mathbf{(x+a)^{2}=x^{2}+2ax+a^{2}}. Use this equation in transforming the equation from step 3 to step 4)

8 0
3 years ago
What is the value of the expression x^2y–y+xy^2–x for x=4 and y=0.25?
stepan [7]

Answer:

0 (zero)

Step-by-step explanation:

{x}^{2} y - y + x {y}^{2}  - x  \\  =  {4}^{2} \times  0.25 - 0.25 + 4 \times  {0.25}^{2}  - 4 \\  = 16 \times  0.25 - 0.25 + 4 \times  0.0625- 4  \\  = 4 - 0.25 + 0.25 - 4 \\  = 0 \\  \\  \purple {\boxed{ \bold{ \therefore \:  {x}^{2} y - y + x {y}^{2}  - x  = 0}}}

8 0
3 years ago
What is the relationship between the bridge strength and bridge thickness?
ivanzaharov [21]
I need more context to answer this question
7 0
2 years ago
A city with a population of 700,000 has been growing at a rate of 2% per year. If this rate continues, what would the population
Mars2501 [29]

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Step-by-step explanation:

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3 0
2 years ago
Which expression is equivalent to xy^2/9?
Law Incorporation [45]

Answer:

xy^\frac{2}{9} = x*\sqrt[9]{y^2}

Step-by-step explanation:

Given

xy^\frac{2}{9}

Required

The equivalent expression (see attachment)

We have:

xy^\frac{2}{9}

Split

xy^\frac{2}{9} = x*y^\frac{2}{9}

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So, we have:

xy^\frac{2}{9} = x*\sqrt[9]{y^2}

<em>Hence (d) is correct</em>

5 0
2 years ago
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