Question

Y=-(x+2)^2-1построить,решение.​

Answer 1

Ответ:

y = -x^2 -4x - 5

Объяснение:

1. у = -(x^2 + 4x + 4) -1

2. y = -x^2 -4x - 4 - 1

3. y = -x^2 -4x - 5

Answer 2

To graph the equation $Y=-(x+2)^2-1$, we'll start by understanding the key features of the equation. The given equation is a quadratic function in the form of $Y=a(x-h)^2+k$, where $(h,k)$ represents the vertex of the parabola. In this case, $h=-2$ and $k=-1$.

Here's the step-by-step process to graph the equation:

Step 1: Determine the vertex The vertex of the parabola is at the point $(-h,k)$, which in this case is $(-(-2), -1) = (2, -1)$.

Step 2: Find the y-intercept The y-intercept is the value of $Y$ when $x=0$. Let's plug $x=0$ into the equation: $Y = -((0+2)^2)-1 = -(2^2)-1 = -(4)-1 = -5$ So, the y-intercept is $(0, -5)$.

Step 3: Find the x-intercept(s) The x-intercept(s) are the values of $x$ when $Y=0$. Let's set $Y$ to zero and solve for $x$: $0 = -((x+2)^2)-1$ $(x+2)^2 = -1$

Since a squared term cannot be negative, there are no real solutions for this equation. This means the parabola does not intersect the x-axis.

Step 4: Determine the axis of symmetry The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two symmetrical halves. It is given by $x=h$, which in this case is $x=-2$.

Step 5: Plot the points and sketch the parabola Using the information we gathered in the previous steps, we can now plot the points and sketch the parabola on the coordinate plane:

• Vertex: $(2, -1)$
• Y-intercept: $(0, -5)$
• Axis of Symmetry: $x = -2$

Now, we can sketch the parabola. Since the coefficient of $x^2$ is negative, the parabola opens downward.

The graph of the equation $Y=-(x+2)^2-1$ will look like this:

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          |    . (2, -1)   <-- Vertex
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----------+-----------------
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          |      . (0, -5)  <-- Y-intercept
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Please note that the parabola will continue indefinitely in both directions, but we only drew a portion of it for illustration purposes.

Keep in mind that graphing software or graphing calculators can help you visualize the graph more accurately and efficiently.