Respuesta :

djtwinx017

Answer:

Standard form:   y = 2x² - 8x + 1

Step-by-step explanation:

We are given the following quadratic function, y = 2(x - 2)² - 7, for which we must transform in its standard form.

Definition:

Quadratic Function in Vertex Form:

The vertex form of a quadratic function is y = a(x - h)² + k (which is the format of the given equation).

  • The vertex of the parabola occurs at point (h, k).
  • The value of "a" determines the direction of the graph's opening (reflection across the x-axis); it also indicates the wideness or narrowness of the graph (vertical stretch or compression).

⇒  If the value of "a" is positive, then the vertex is its minimum or lowest point on the graph.

⇒  If the value of "a" is negative, then the vertex is the maximum or highest point  on the graph.

Quadratic Function in Standard Form:

The standard form of a quadratic function is y = ax² + bx + c, where a ≠ 0.

 

Solution:

Step 1: Expand the binomial, (x - 2)²:

The first step in rewriting the given equation into its standard form  is expanding the binomial using the FOIL method, which transforms it into a perfect square trinomial.  

y = 2(x - 2)² - 7

       ⇒   (x - 2)(x - 2)

       ⇒   [ x² - 2x - 2x + 4 ]

Step 2: Substitute the perfect square trinomial into the vertex form:

y = 2(x - 2)² - 7

y = 2(x² - 2x - 2x + 4) - 7

Step 3: Distribute "2" into the parenthesis:

y = 2(x² - 2x - 2x + 4) - 7

y = 2x² - 4x - 4x + 8 - 7

Step 4: Combine like terms and constants, then simplify:

y = 2x² - 8x + 1.

Final Answer:

Therefore, the quadratic function in standard form is y = 2x² - 8x + 1, where a = 2, b = -8, and c = 1.

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Keywords:

Quadratic equations

Parabola

Quadratic functions

Vertex form

Functions

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Learn more about quadratic functions here:

https://brainly.com/question/18797214

BasketballEinstein

Answer:

[tex]\displaystyle y = 2x^2 - 8x + 1[/tex]

Step-by-step explanation:

All you are doing is perfourming order of operations and using the Distributive Property. Here is how it is done:

[tex]\displaystyle y = 2(x - 2)^2 - 7 \hookrightarrow y = 2(x^2 - 4x + 4) - 7 \hookrightarrow y = 2x^2 - 8x + 8 - 7 \\ \\ \boxed{y = 2x^2 - 8x + 1}[/tex]

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