Mathematics: Rewrite the quadratic function in vertex form. y=2x^2+4x-1

Rewrite the quadratic function in vertex form.

Ответ:

hilljade45

07.01.2022

Mathematics

$\large\boxed{y=2(x+1)^2-3}$

Step-by-step explanation:

The vertex form of an equation of a parabola:

y=a(x-h)^2+k

(h, k) - vertex

We have

$y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)$

We must use the formula: $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)$

Use the distributive formula a(b + c) = ab + ac

$2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3$

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Ответ:

lilbit217

20.10.2021

Mathematics

I believe the answer is: Prices for goods and services increased, and a dollar bought less than it previously had

In the 1970s, united states was experiencing a period of economic stagnation which later known as called the great inflation of the 1970s.

During this period, the number of unemployment skyrocketed and the value of our currency fall dramatically, which caused an increase in overall products and less amount of products it can obtain with previously same amount.

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Rewrite the quadratic function in vertex form.
y=2x^2+4x-1

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