Mathematics, 10.02.2022 22:30 lucywood2024

Re-write the quadratic function below in Standard Form
y= 2(x - 2)2 – 7

Answers: 1

Show answers

Answers

Answer from: sunshine52577oyeor9

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

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

Keywords:

Quadratic equations

Parabola

Quadratic functions

Vertex form

Functions

Learn more about quadratic functions here:

Answer from: Quest

$a^b=\underbrace{a\cdot a\cdot \ldots \cdot a}_{b}$

a - base

b - exponent

$8^3=\underbrace{8\cdot 8 \cdot 8}_{3}$

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8

Answer from: Quest

20%

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Explain how you can use the associative property to evaluate (7x50)x4.

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Kayla and alberto are selling fruit for a school fundraiser. customers can buy small boxes of grapefruit and large boxes of grapefruit. kayla sold 3 small boxes of grapefruit and 1 large box of grapefruit for a total of $65. alberto sold 1 small box of grapefruit and 1 large box of grapefruit for a total of $55. what is the cost each of one small box of grapefruit and one large box of grapefruit?

Answers: 1

Answer

Mathematics, 21.06.2019 22:40

How many verticies does a triangular prims have

Answers: 2

Answer

Mathematics, 21.06.2019 23:10

Carly stated, “all pairs of rectangles are dilations.” which pair of rectangles would prove that carly’s statement is incorrect?

Answers: 1

Answer

You know the right answer?

Re-write the quadratic function below in Standard Form
y= 2(x - 2)2 – 7...