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3 years ago

F(x) = 2(x - 3)^2 - 2

Mathematics

1 answer:

Natali5045456 [20]3 years ago

4 0

Hi. I was unsure of what exactly you wanted from this equation, so here's a quick analysis:

Domain: (-∞, ∞)

Range: (-2, ∞)

X-intercepts: (4, 0), (2, 0)

Y-intercept: (0, 16)

Axis of Symmetry: x = 3

Minimum value (vertex): (3, -2)

Standard form: y = 2x^2 - 12x + 16

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A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a func

Gemiola [76]

Answer:

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

Step-by-step explanation:

The height is given by the following function:

$f(x) = -16x^{2} + 200x$

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

If $\bigtriangleup < 0$ , the polynomial has no solutions.

In this question:

$f(x) = -16x^{2} + 200x$

$-16x^{2} + 200x = 612$

$16x^{2} - 200x + 612 = 0$

We have to find $\bigtriangleup$

We have that $a = 16, b = -200, c = 612$ . So

$\bigtriangleup = (-200)^{2} - 4*16*612 = 832$

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

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Find the geometric mean of 50 and 4

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Mean also means average.

$\frac{50+4}{2}=\frac{54}{2} =27$

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Answer:

y=-x+3.

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