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3 years ago

The graph of quadric function has a minumum at (-2,-3) and passes through the point (2,13)

Mathematics

1 answer:

Leto [7]3 years ago

3 0

Answer:

g(x) = x² + 4x + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 2, - 3), thus

y = a(x + 2)² - 3

To find a substitute (2, 13) into the equation

13 = a(2 + 2)² - 3

13 = 16a - 3 ( add 3 to both sides )

16 = 16a ( divide both sides by 16 )

a = 1, hence

g(x) = (x + 2)² - 3 ← expand factor and simplify

= x² + 4x + 4 - 3

g(x) = x² + 4x + 1

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Answer:

$40.25$ inches

Step-by-step explanation:

Following what the problem mentions:

"eric is 70 inches tall"

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Convert this number given in standard form into scientific notation. 0. 0000069 What is the value in scientific notation? 0. 69

Len [333]

Scientific notation is used so that the order of the number is known in first glance. The value of the given number in scientific notation is given by: Option B: $6.9 \times 10^{-6}$

<h3>How does scientific notations work?</h3>

The number is written in the form $a \times 10^b$ where we have $1 \leq a < 10$

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations have some of the profits as:

Better readability due to compact representation
Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

For the given case, the number in consideration is 0.0000069

Rewriting it in fraction form, we get:

$0.0000069 = \dfrac{69}{10000000} = \dfrac{69}{10^7} = 69 \times 10^{-7} = 6.9 \times 10 \times 10^{-7}\\\\0.0000069 = 6.9 \time 10 ^{-7 +1} \\0.0000069 = 6.9\times 10^{-6}$