12. Which function is a quadratic function?
A. y=3x^2+x
B. y=2x-1
C. y=3/x
D. y= -|x|
Which function rule represents the data in the table?
x -3, -2, -1, 0, 1
y 1, -2, -5, -8, -11
A. y=-3x-8
B. y=1/3x -8
C. y=1/3x+8
D. y=3x+8
a quadratic has x^2 as its highest power. So, A.
Note that y decreases by 3 when x increases by 1. So, it will look like
y = -3x
But, when x=0, -3x=0, and y is -8. So,
y = -3x-8
again, A
A. y=3x^2+x is a quadratic function.
The function rule that represents the data in the table is D. y=3x+8. Because when you substitute the given values of x (-3, -2, -1, 0, 1) into the equation y=3x+8, you will get the corresponding values of y (1, -2, -5, -8, -11) from the table.
A. y=3x^2+x
To determine if a function is quadratic, we need to check its degree. Quadratic functions have a degree of 2, which means the highest power of the variable is 2.
Let's analyze each function:
A. y=3x^2+x
This function has a degree of 2 (the term with the highest power of x is x^2), so it is a quadratic function.
B. y=2x-1
This function has a degree of 1 (the term with the highest power of x is x), so it is not a quadratic function.
C. y=3/x
This function contains a variable in the denominator. Quadratic functions do not have variables in the denominator, so it is not a quadratic function.
D. y= -|x|
This function does not contain any squared terms, so it is not a quadratic function.
Therefore, the quadratic function is option A: y=3x^2+x.
Now let's analyze the table of data:
x -3, -2, -1, 0, 1
y 1, -2, -5, -8, -11
To find the function rule that represents the data, we need to identify the pattern or relationship between the x-values and y-values.
By examining the data, we can see that as x increases by 1, y decreases by 3. This indicates a linear relationship with a slope of -3.
To find the y-intercept, we can choose any point from the table. Let's take the point (0, -8).
Using the slope-intercept form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, we can substitute the values:
-8 = -3(0) + b
-8 = b
So the y-intercept is -8.
Therefore, the function rule that represents the data in the table is:
y = -3x - 8.
Therefore, the correct answer is A: y = -3x - 8.
is #12 D?
is #15 B?