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vekshin1
2 years ago
5

Write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)

Mathematics
1 answer:
dsp732 years ago
5 0

Answer:

f(x) = -19/9(x + 3)² + 5

Step-by-step explanation:

Given the vertex, (-3, 5) and the point, (0, 14):

Use the following quadratic equation formula in vertex form:

f(x) = a(x - h)² + k

where:

(h, k) = vertex

a = determines whether the graph opens up or down, and makes the graph wide or narrow.

<em>h</em><em> </em>= determines how far left or right the parent function is translated.

<em>k</em> =  determines how far up or down the parent function is translated.

Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for <em>a</em>:

f(x) = a(x - h)² + k

14 = a(0 + 3)² + 5

14 = a(3)² + 5

14 = a(9) + 5

Subtract 5 from both sides:

-14 - 5 = 9a

-19 = 9a

Divide both sides by 9 to solve for a:

-19/9 = 9a/9

-19/9 = a

Therefore, the quadratic function in vertex form is:

f(x) = -19/9(x + 3)² + 5

Please mark my answers as the Brainliest, if you find this helpful :)

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GalinKa [24]

Answer:

The intersection is (\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2}).

The Problem:

What is the intersection point of y=\log(x) and y=\frac{1}{2}\log(x+1)?

Step-by-step explanation:

To find the intersection of y=\log(x) and y=\frac{1}{2}\log(x+1), we will need to find when they have a common point; when their x and y are the same.

Let's start with setting the y's equal to find those x's for which the y's are the same.

\log(x)=\frac{1}{2}\log(x+1)

By power rule:

\log(x)=\log((x+1)^\frac{1}{2})

Since \log(u)=\log(v) implies u=v:

x=(x+1)^\frac{1}{2}

Squaring both sides to get rid of the fraction exponent:

x^2=x+1

This is a quadratic equation.

Subtract (x+1) on both sides:

x^2-(x+1)=0

x^2-x-1=0

Comparing this to ax^2+bx+c=0 we see the following:

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c=-1

Let's plug them into the quadratic formula:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}

x=\frac{1 \pm \sqrt{1+4}}{2}

x=\frac{1 \pm \sqrt{5}}{2}

So we have the solutions to the quadratic equation are:

x=\frac{1+\sqrt{5}}{2} or x=\frac{1-\sqrt{5}}{2}.

The second solution definitely gives at least one of the logarithm equation problems.

Example: \log(x) has problems when x \le 0 and so the second solution is a problem.

So the x where the equations intersect is at x=\frac{1+\sqrt{5}}{2}.

Let's find the y-coordinate.

You may use either equation.

I choose y=\log(x).

y=\log(\frac{1+\sqrt{5}}{2})

The intersection is (\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2}).

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Answer:

See Below:

Step-by-step explanation:

40,000*8/25= the diameter, because the diameter is 8/25 of the equator which is 40000

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1. Let C be between D and E. Use the Segment addition Postulate to solve for v.
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By applying the segment addition postulate, the <u>value of v = 7</u>

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  • Therefore, by substitution, we will have the following equation:

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Therefore, using the segment addition postulate, the <u>value of v = 10</u>

Learn more about the segment addition postulate here:

brainly.com/question/1721582

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