1.) graph the function and identify the domain and range. y=-4x^2
anyone wanna help me? the test is death. its the Quadratic functions and equations one. Thanks!
Oh, I'm here to help, and hopefully lighten the mood a bit too! Let's tackle this quadratic function together.
First, let's start with the graph. The function is y = -4x^2. Since it's a quadratic function, its graph will be a downward opening parabola. The negative coefficient in front of x^2 tells us that it's going to be an inverted smiley face (or a frowny face if you prefer).
As for the domain, you can plug in any real number for x. So, the domain of this function is all real numbers, from negative infinity to positive infinity. It's like you have a never-ending supply of x-values to work with.
Now, let's talk about the range. Since the coefficient in front of x^2 is negative, the parabola will open downwards and stretch towards negative infinity. In other words, the range will be all real numbers less than or equal to the maximum point of the parabola.
So, to summarize:
- The graph is a downward opening parabola.
- The domain is all real numbers.
- The range is all real numbers less than or equal to the maximum point.
Good luck with your quadratic functions and equations test! Remember, even if the test seems intimidating, just approach it one step at a time, and you'll do great.
To graph the function y = -4x^2, start by creating a table of values by choosing different values for x and calculating the corresponding y-values.
Let's start with x = -2:
y = -4(-2)^2 = -4(4) = -16
When x = -1:
y = -4(-1)^2 = -4(1) = -4
For x = 0:
y = -4(0)^2 = -4(0) = 0
For x = 1:
y = -4(1)^2 = -4(1) = -4
When x = 2:
y = -4(2)^2 = -4(4) = -16
Now, let's plot these points on a graph:
(-2, -16), (-1, -4), (0, 0), (1, -4), (2, -16)
When we connect these points, it will form a downward-opening parabola.
The domain of this function is all real numbers since any value of x can be squared and multiplied by -4.
The range is all y-values less than or equal to 0 since the parabola opens downwards and its vertex is at (0, 0).
Sure, I can help you with that! To graph the function y = -4x^2, we can start by creating a table of values.
Let's choose a few convenient x-values, such as -2, -1, 0, 1, and 2. We'll substitute these values into the equation to find the corresponding y-values.
When x = -2: y = -4(-2)^2 = -4(4) = -16
When x = -1: y = -4(-1)^2 = -4(1) = -4
When x = 0: y = -4(0)^2 = 0
When x = 1: y = -4(1)^2 = -4(1) = -4
When x = 2: y = -4(2)^2 = -4(4) = -16
Now, we can plot these points on a graph:
(-2, -16), (-1, -4), (0, 0), (1, -4), (2, -16)
To sketch the graph, we can connect these points smoothly. Since the coefficient of x^2 is negative, the graph opens downwards like a "U" shape. It will be symmetric with respect to the y-axis.
The domain of the function is all real numbers because any value of x can be squared.
The range of the function is all real numbers less than or equal to 0 because the function never goes above or touches the x-axis.
I hope this helps you understand how to graph the function and identify its domain and range! Good luck on your test!
The domain of a function is the set of all allowable values of the independent variable, in this case x-values.
The range of a function is the set of output values when all x-values in the domain are evaluated into the function, in this case the y-values.
In this case written with interval notation the domain is x ∈ ( - ∞ , ∞ )
because all these numbers can be squared
OR
x ∈ R
written with set notation
This means all real numbers.
In this case the rage is y ∈ ( - ∞ , 0 ) written with interval notation
OR
y ∈ ≤ 0
written with set notation
This is because the square of a number is always positive, but when multiplied by - 4 then it is always negative.
For a graph on the Internet find some site for drawing graphs.
There are many of them.