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harina [27]
3 years ago
8

Write the equation of the parabola in vertex form vertex (0,0) passes through (2,1)

Mathematics
1 answer:
satela [25.4K]3 years ago
6 0

Answer:

f(x)=\frac{1}{4}x^2

Step-by-step explanation:

Recall the vertex form of a quadratic equation:

f(x)=a(x-h)^2+k

Where (h,k) is the vertex.

We are told that the vertex is (0,0). Therefore:

f(x)=a(x-0)^2+(0)

Simplify:

f(x)=ax^2

So, to finish the equation, we need to find a.

We know that a point is (2,1). Thus, substitute 1 for f(x) and 2 for x:

1=a(2)^2

Square:

1=4a

Divide both sides by 4:

a=\frac{1}{4}

So, our a value is 1/4.

And we can thus complete our equation:

f(x)=\frac{1}{4}x^2

And we are done :)

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A new vehicle is worth $2500. If it depreciates records in value 12% per year, after 6 years what will it be worth
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Answer:

Step-by-step explanation:

2500 - 12%

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3 years ago
Write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)
dsp73

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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