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4 years ago

3. What are the coordinates of the vertex of the graph of the function y = –3x² –12x + 3? (1 point

Mathematics

2 answers:

Snezhnost [94]4 years ago

7 0

Answer:

Vertex of the given function is (-2,15)

Step-by-step explanation:

The given equation is $y=-3x^2-12x+3$

It is a quadratic equation and we know that a quadratic equation represents a parabola. Hence, we find the vertex of the parabola.

The general equation of a quadratic equation is $y=ax^2+bx+c$

Comparing this equation with the given equation

a = -3, b = -12, c = 3

Now, the x coordinate of the vertex is

$-\frac{b}{2a}\\\\=\frac{-(-12)}{2\cdot(-3)}\\\\=-2$

Now, the y coordinate of the vertex is

$y(-2)=-3(-2)^2-12(-2)+3\\\\=-12+24+3\\\\=15$

Therefore, the vertex of the given function is (-2,15)

insens350 [35]4 years ago

6 0

The function y = –3x² –12x + 3 is a parabola facing either upward of downward. we use completing the squares to find the vertex.

y = -3(x² + 4x + 1)

(k/2)^2 = (4/2)^2 = 4
y = -3(x² + 4x + 4 + 1 - 4)

y = -3(x + 2)² + 9
y- 9 = -3(x + 2)²
vertex is equal to at (-2,9)

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3 years ago

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3 years ago

If xy + y² = 6, then the value of dy/dx at x= -1 is

mylen [45]

Hi there!

$\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}$

$\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}$

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx) + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

y² - y - 6 = 0

(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

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4 years ago