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Katena32 [7]
3 years ago
11

Write an equation of the parabola in vertex form

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Step-by-step explanation:

Recall that a parabola is the graph representing a quadratic equation, which is standard form is as follows:

y = ax2 + bx + c

where the value of 'a' determines whether the parabola opens upwards of downwards (i.e., the parabola opens upwards if a>0 and opens downwards if a<0) and the axis of symmetry is given by the line x = -b/(2a).

The vertex form of a parabola's (or a quadratic) equations is given by the following formula:

y = a(x - h)2 + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.

Given that the vertex is at (0, 3), then ..... h = 0 and k = 3 ..... thus,

y = a(x - 0)2 + 3

y = a(x)2 + 3

With a point at (-4, -45), then ..... x = -4 and y = -45 ..... therefore,

-45 = a(-4)2 + 3

-45 = a(16) + 3

Solve for a by first subtracting 3 from both sides of the equation then dividing both sides of the equation by 16:

-45 - 3 = a(16) + 3 - 3

-48 = a(16)

-48/16 = 16a/16

-3 = a

With a vertex (h, k) at (0, 3) and given that a = -3, then the equation of this parabola in vertex form is as follows:

y = a(x - h)2 + k

y = -3(x - 0)2 + 3

y = -3x2 + 3

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vladimir1956 [14]

<u>Part (a)</u>

The variable y is the dependent variable and the variable x is the independent variable.

<u>Part (b)</u>

The cost of one ticket is $1.25. Therefore, the cost of 25 tickets will be: .

Now, we know that Johnny spent his money only on ride tickets and fair admission and that he spent a total of $43.75.

Therefore, the price of the fair admission is: $43.75-$31.25=$12.5

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be  written as:

y=1.25x+12.5......Equation 1

<u>Part (c)</u>

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 1.25x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$12.5.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.

7 0
3 years ago
The area of a polygon is the number of square units contained in its interior true or false
Vsevolod [243]
<span>False. Perimeter is a linear measure. Square units are for area.</span>
5 0
3 years ago
Help find x out of these 4 questions i can’t find the answer anywheew
babunello [35]

Answer:

Option D. 11√6/2

Step-by-step explanation:

We'll begin by calculating the side opposite to angle 60°.

This is illustrated below:

Angle θ = 60°

Opposite =?

Hypothenus = 11

Using the sine ratio, we can obtain the side opposite to angle 60° as follow:

Sine θ = Opposite/Hypothenus

Sine 60 = Opposite /11

Cross multiply

Opposite = 11 × Sine 60

Sine 60 = √3/2

Opposite = 11 × √3/2

Opposite = 11√3/2

Finally, we shall determine the value of x as follow:

Angle θ = 45°

Opposite = 11√3/2

Hypothenus = x

Using the sine ratio, we can obtain the value of x as shown below:

Sine θ = Opposite/Hypothenus

Sine 45° = 11√3/2 /x

Cross multiply

x × Sine 45° = 11√3/2

Sine 45° = 1/√2

x × 1/√2 = 11√3/2

x/√2 = 11√3/2

Multiply through by √2

x = √2 × 11√3/2

x = 11√6/2

4 0
3 years ago
A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is
Svetllana [295]

Answer:

Option D.

Step-by-step explanation:

Suppose that we have a set of N values:

{x₁, x₂, ..., xₙ}

The median is the value in the middle, and the mean is calculated as:

M = \frac{(x_1 + x_2 + x_3 ... + x_n)}{N}

Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k"  (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)

Now we add 7 to all the values greater than the median

We subtract 7 to all values smaller than the median.

Then the median remains unchanged (because we did not add nor subtract anything to the median).

The new mean will be:

M' = \frac{(x_1 - 7) + (x_2 - 7) + ... + (x_{k}) + ... + (x_n + 7)}{N} = \frac{(x_1 + x_2 + ... + x_n) + (-7)*(n/2 - 0.5) + 7*(n/2 - 0.5)}{N}  = \frac{(x_1 + x_2 + ... + x_n)}{N} = M

So the mean does not change.

Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.

Finally, the standard deviation is computed as:

SD = \sqrt{\frac{(x_1 - M)^2 + ... + (xn - M)^2}{N} }

Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)

Then the only value that does not have the same value in both the original and new data sets is the standard deviation.

6 0
3 years ago
Plz g0ive me solution
Serga [27]

Answer:

separate the x from the numbers it will make the equation easier

8 0
2 years ago
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