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2 years ago

Can anyone tell me what this graph is in slope intercept form?

Mathematics

1 answer:

Eddi Din [679]2 years ago

6 0

Answer:

the standard form equation is 1/2x^2-x-3/2=0

the vertex form equation is 1/2(x-1)^2-2=0

Step-by-step explanation:

Unfortunately, this can't be written in slope intercept form but I can write it in standard form(ax^2+bx+c) or vertex form (a(x-h)+k)

The vertex is (1,-2)

I estimate a=1/2 because the graph was widened and that can only be done by a fraction.

So, 1/2(x-1)^2-2=0

To find it in standard form

foil (x-1)(x-1)= x^2-2x+1

Then multiply by 1/2(x^2-2x+1)= 1/2x^2-x+1/2-2

To add 1/2-2. You mulitply -2 by 2/2 which equals 1/2-4/2 which equals -3/2

So the standard form equation is 1/2x^2-x-3/2=0

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the point of M ( a, 4 ) is the midpoint of the line segment with endpoint at A(1,3) and B(5,b). Find the value of a and b

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The value of a and b from the coordinates are 3 and 5 respectively

<h3>Midpoint of coordinates</h3>

The formula for finding the midpoint of two coordinates is expressed as;

M(x, y) = {x1+x2/2, y1+y1/2}

Given the following coordinates

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Using the formula

a = 1+5/2

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a = 3

Similarly

4 = 3+b/2

8 = 3+b

b = 8-3

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Hence the value of a and b from the coordinates are 3 and 5 respectively

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Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

$|u|=\sqrt{14^2+9^2}$ which is $\sqrt{277}$

$|v|=\sqrt{3^2+6^2}$ which is $\sqrt{45}$

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

$cos\theta=\frac{uv}{|u||v|}$ where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

$cos^{-1}\theta=\frac{96}{111.64676}$ which returns an angle measure of 30.7. Plugging that all into the dot product formula:

$u*v=\sqrt{277}*\sqrt{45}cos(30.7)$ gives you a dot product of 96

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