What is the domain and range of the equation y=-x^2-4x-7?
It is a parabola in standard position
so anything goes for x
find the vertex, the range ≥ the y-value of that vertex.
How?? What are the equations?
work
pls can you helpme withh domain and range
To determine the domain and range of the equation y = -x^2 - 4x - 7, let's break down each term and understand its impact on the graph.
The domain refers to all possible values that x can take in the equation. In this case, there are no specific restrictions on the values of x since it can take any real number. Therefore, the domain is (-∞, +∞), representing all real numbers.
Now, let's analyze the range, which represents all possible values that y can take. To find the range, we need to consider the shape and direction of the graph.
The given equation is y = -x^2 - 4x - 7, which is a quadratic function in the form of y = ax^2 + bx + c. The coefficient "a" is negative, which means the graph opens downwards and has a maximum point.
To determine the range, first, let's find the vertex of the parabola, which is the maximum point.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a).
Here, a = -1 and b = -4.
Substituting these values into the formula, we have x = -(-4) / (2 * -1), which simplifies to x = 4 / (-2) = -2.
To find the y-coordinate of the vertex, substitute x = -2 into the equation:
y = -(-2)^2 - 4(-2) - 7
= -4 + 8 - 7
= -3
Thus, the vertex is (-2, -3).
Since the parabola opens downwards from the vertex (-2, -3), the range is all values of y less than or equal to -3. Therefore, the range is (-∞, -3] which represents all real numbers less than or equal to -3.