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3 years ago

14

Find the vertex for this function. f(x)=-2x^2+8x-11

1 answer:

loris [4]3 years ago

3 0

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{-11} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{8}{2(-2)}~~,~~-11-\cfrac{8^2}{4(-2)} \right)\implies \left( 2~~,~~-11+\cfrac{64}{8} \right) \\\\\\ (2~~,~~-11+8)\implies (2~~,~~-3)$

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Find the distance between (-2, 8) and (11, 2). Round to the nearest hundredth.

andrew11 [14]

Answer: 14.32 units

Step-by-step explanation:

The formula for calculate the distance between two points is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, given the points (-2,8) and (11,2), we can identify that:

$x_2=11\\x_1=-2\\\\y_2=2\\y_1=8$

Therefore, we just need to substitute values into the formula in order to calculate the distance between the given points. This is (Rounded to the nearest hundred):

$d=\sqrt{(11-(-2))^2+(2-8)^2}\\\\d=14.32\ units$

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4 years ago

Given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2+49a+108$ and $2a+9$.

Shtirlitz [24]

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Step-by-step explanation:

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4 years ago

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Select all the equations that are true when x = 4

V125BC [204]

Answer:

B and E

Step-by-step explanation:

A. 8x = 2

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C. 40/x = 5

40/4 = 5

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3 years ago

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Sergio039 [100]

Step-by-step explanation:

1.

Subtract the coefficient from both sides, keep 55 on the same side.

${x}^{2} - 6x = 55$

Complete the square by dividing the coefficient by two and squaring it.

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Use binomial to factor the left side.

$(x - 3) {}^{2} = 64$

2. Solve for x.

$(x - 3) = 8$

$x = 11$

Remeber the square root of 64 is also -8 so

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$x = - 5$

So the solutions are -5 and 11

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3 years ago

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