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Elodia [21]
2 years ago
6

1.) Determine the type of solutions for the function (Picture 1)

Mathematics
1 answer:
NNADVOKAT [17]2 years ago
7 0

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

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T(x)=1-2x how do you graph this problem
Eva8 [605]

Answer:

Explained

Step-by-step explanation:

The 1 is the y-intercept

The -2 is the slope

First place a point at (0,1)

Then, because it's negative from left to right the graph is decreasing (going lower on the y-axis the farther you go on the x-axis).

Slope is rise over run so the -2 affects how far it goes. So for each value of x that increases by one, a new point will be two units down and one unit right of the previous point. To graph to the left of the y-intercept then you do that backwards where the next point is two units up and one unit left.


Then just draw a straight line connecting all the points.

7 0
3 years ago
Need help plz I’m almost done
JulsSmile [24]

Hello!


The graph, (2/5)^x is an exponential function.


Since there is not a negative symbol in the front of the function, options A and B are incorrect.


For option 3 to be correct, there would need to be a negative symbol in front of the exponent, x.


So therefore, the answer option 4. (Also, I'll post a graph. :))


8 0
3 years ago
The flower shop sold roses and tulips. The number of roses sold was 5 less than twice the number of tulips sold. If the shop sol
LenaWriter [7]

Answer: the number of roses sold is 69 while number of tulips is 37

Step-by-step explanation:

Let x represent the number of roses that the flower shop sold.

Let y represent the number of tulips that the flower shop sold.

The number of roses sold was 5 less than twice the number of tulips sold. This means that

x = 2y - 5 - - -- -- - - - - - ;1

If the shop sold 106 flowers in total, it means that

x + y = 106

Substituting x = 106 - y into equation 1, it becomes

106 - y = 2y - 5

3y = 106 + 5 = 111

y = 111/3 = 37

x = 106 - y = 106 - 37

x = 69

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3 years ago
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Answer:

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3 years ago
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andriy [413]
The answer is A i believe
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3 years ago
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