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3 years ago

Consider the function: f(x) = 2x^2 - 1.5x - 5 and its graph.

Mathematics

1 answer:

Dominik [7]3 years ago

5 0

Answer:

f(x) = -4x² + 19x - 18

Step-by-step explanation:

$f(x) = 2x^2 - 1.5x - 5$

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

$y=f(x-2) = 2(x-2)^2 - 1.5(x-2) - 5\\y = 2(x^2-4x+4) - 1.5x+3 - 5\\y=2x^2-8x+8-1.5x+3-5\\y=2x^2-9.5x+6$

f(x) = 2x² - 9.5x + 6

If it is then translated 3 units in the positive y, we add 3 to the input function to get:

$y=f(x)+3=2x^2-9.5x+6+3\\y = 2x^2-9.5x+9$

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

$y =2( 2x^2-9.5x+9) = 4x^2-19x+18\\y= 4x^2-19x+18$

iii) reflected across the x-axis

we multiply the parent function by –1, to get a reflection about the x-axis.

$y= -1(4x^2-19x+18)=-4x^2+19x-18\\y=f(x)=-4x^2+19x-18$

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The price in dollars per gallon is 4.02 dollars per gallons.

<h3>How to find the price of gasoline in dollars per gallon?</h3>

Gasoline costs 1.05 euro per litre in France.

The first thing to do is to determine the equivalent amount of the same litre in dollar while in France.

Then, equate it the quantity of litres to gallons.

Hence,

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cross multiply

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price = 1.0605 dollars

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Therefore,

cost = 1.0605 / 0.264172

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Therefore, the price in dollars per gallon is 4.02 dollars per gallons.

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2 years ago

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step by step solution:

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3 years ago

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Vladimir79 [104]

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Step-by-step explanation:

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3 years ago

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RideAnS [48]

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H is not included because it falls on the dotted line. Any point that falls on a dotted line does not satisfy both inequalities.

If the line were solid however, then the point would satisfy both inequalities. This is because the line would include the greater than or equal to symbol "≥" which means that the point could equal to 8 or be less than 8. Since the symbol is not used, it doesn't satisfy both equations.