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3 years ago

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

Mathematics

1 answer:

Fantom [35]3 years ago

5 0

Answer:

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

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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4 years ago

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<h3>Answer:</h3>

Difference between Mercury's and Neptune's distance from the sun is $4.443 \times 10^9 \text{ km }$

<h3>Solution:</h3>

Given that,

Distance of mercury from sun = 57, 000, 000 km

Distance of Neptune from sun = $4.5 \times 10^9 \text{ km }$

To find: Difference between Mercury's and Neptune's distance from the sun

Let us convert distance of mercury from sun to scientific notation

Scientific notation is used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits

Steps to remember:

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b

$57, 000, 000 = 5.7 \times 10^7$

Therefore,

Distance of mercury from sun = $5.7 \times 10^7 \text{ km }$

Calculating difference between Mercury's and Neptune's distance from the sun:

difference = Distance of Neptune from sun - Distance of mercury from sun

$\text{ difference } = (4.5 \times 10^9) - (5.7 \times 10^7)$

Let us make both powers same

$\text{ difference } = (4.5 \times 10^9) - (0.057 \times 10^9)$

Taking 10 power 9 common we get,

$\text{ difference } = 10^9(4.5-0.057)\\\\\text{ difference } = 10^9 \times (4.443)\\\\\text{ difference } = 4.443 \times 10^9$

Thus difference between Mercury's and Neptune's distance from the sun is $4.443 \times 10^9 \text{ km }$

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3 years ago

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Step-by-step explanation:

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