Mathematics, 10.02.2022 22:30, lucywood2024

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

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answered: 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:

answered: Guest

$\dfrac{p}{4}$ or $\dfrac{1}{4}p$

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is $\dfrac{p}{4}$ or $\dfrac{1}{4}p$

answered: Guest

he has now walked a total of what?

if i know what this is maybe i can

step-by-step explanation:

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