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Ronch [10]
3 years ago
6

The standard form of the equation of a parabola is y = 5x2 + 20x + 14.

Mathematics
2 answers:
Irina-Kira [14]3 years ago
8 0
The vertex form of quadratic equation is expressed as:

y = a (x - h)² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y- 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x +4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2)²

We can now manipulate further the equation above in the vertex form. Thus,

y= 5 [ x- (-2)]² - 6
Ber [7]3 years ago
7 0

Answer:

y = 5(x+2)^2 - 6

Step-by-step explanation:

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Pls help! 50 POINTS!
nirvana33 [79]

Answer:

See below.

Step-by-step explanation:

1)

So we have the equation:

2x+3y=1470

To change into the slope-intercept form, we need to isolate the y-variable. Thus, subtract 2x from both sides:

(2x+3y)-2x=(1470)-2x

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Now, divide both sides by 3. The left side cancels:

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y=mx+b

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Thus, the slope is -2/3 and the y-intercept is 490.

2)

So, since we already know the y-intercept is 490, plot a point at (0,490).

The slope is too small to use. Thus, multiply the fraction by 100. It is now (-200/300). This means that we move <em>down</em> 200 for every 300 (recall that the slope means rise over run. Thus, we move down 200 for every 300 to the right). Thus, another possible point would be (0+300,490-200) or (300,290). Plot that. Then, connect them.

3)

To write in in function notation, simply substitute the y-variable for the function notation. Our independent variable here is x so we'll use that.

y=-\frac{2}{3}x+490\\ f(x)=-\frac{2}{3}x+490

This means that for every x sandwiches made, there is f(x) wraps made for the total sum to be $1,470.

For example, if 105 sandwiches were made, then f(105)=-2/3(105)+490=420 wraps were made for the total profit to be $1,470.

4)

Please refer to the attached graph.

5)

First, since the total profit has now increased, the graph above and to the right of the old graph. This is because Sal needs to sell more sandwiches and wraps. Likewise, because of this, the x- and y-intercepts will also be different. Nevertheless, if converted into the slope-intercept equation, the slope will remain the same.

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What is the solution to the equation –10.3+y = 5.2?
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First, regroup the terms. / Your problem should look like: y - 10.3 = 5.2
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Answer:

112

Step-by-step explanation:

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