For quadratic functions having the folllowing properties: Look at photo

Mathematics

1 answer:

iVinArrow [24]2 years ago

7 0

Answer:

f(x) = -4x²+24x -28

Step-by-step explanation:

The given zeros are a sum and a difference. You can use the special factoring of the product of a sum and difference to simplify the product of the factors of the quadratic. Each zero 'p' corresponds to a factor (x -p):

f(x) = a(x -(3 +√2))(x -(3 -√2)) = a((x -3)² -(√2)²) = a((x -3)² -2)

We can find the leading coefficient 'a' from the given point:

f(1) = -8 = a((1 -3)² -2) = 2a

a = -8/2 = -4

Then the function can be written as ...

f(x) = -4((x -3)² -2) = -4(x² -6x +9 -2)

f(x) = -4x²+24x -28

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I'm really not sure how to go about solving this algebraic equation, please help! .513 = (2x)^2 / (.05-x)

LiRa [457]

Let's set it up like this:
$0.513=\frac{\left(2x\right)^2}{\left(0.05-x\right)}$
Multiply both sides by $0.05-x$
$0.513\left(0.05-x\right)=\frac{\left(2x\right)^2}{0.05-x}\left(0.05-x\right)$
$0.513\left(0.05-x\right)=4x^2$
We are then going to use the distributive property. Since we also know that the opposite of an number that is squared is the square root, we can also apply that. We would be left with something like this:
$x=-\frac{0.513+\sqrt{0.673569}}{8},\:x=\frac{\sqrt{0.673569}-0.513}{8}$
The variable $x$ can be both positive or negative.
We have found successfully our answer.

Let me know if you have any questions regarding this problem!
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4 0

3 years ago

Mrs. Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to dri

algol [13]

Answer:

C = 0.97m
$1164 for 1200 miles
845 miles for $820

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

$485/(500 mi) = $0.97 /mi

<h3>Equation</h3>

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

C = 0.97m . . . . . where C is cost in dollars for m miles driven

<h3>1200 miles</h3>

The cost for driving $1200 miles will be ...

C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

820 = 0.97m

m = 820/0.97 = 845.36