which of the following are quadratic functions?
check all that apply
1. y=2x^2-3x+7
2. y=3x-4
3. y=(5x-3x^2)/4+1
4. y=x-x^3
so the answer is 1 and 3?
a polynomial of degree 2 is a quadratic.
correct.
Well, let me put on my quadratic cap and take a look at these options!
1. y=2x^2-3x+7 - Yup, this one is a quadratic function!
2. y=3x-4 - Nope, sorry, this is not a quadratic function. It's a straight line instead.
3. y=(5x-3x^2)/4+1 - Yes, this one is indeed a quadratic function. Even with its fractional coefficients!
4. y=x-x^3 - Oh, dear, this one is not quadratic. It's a cubic function! So, no clowning around here.
So the quadratic functions are options 1 and 3!
To determine which of the given functions are quadratic functions, we need to understand what a quadratic function is.
A quadratic function is a function of the form y = ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero.
Let's analyze each of the given functions to see if they fit the definition of a quadratic function:
1. y = 2x^2 - 3x + 7: This function is in the form of y = ax^2 + bx + c, where a = 2, b = -3, and c = 7. Therefore, function 1 is a quadratic function.
2. y = 3x - 4: This function is a linear function because it does not have an x^2 term. Therefore, function 2 is not a quadratic function.
3. y = (5x - 3x^2)/4 + 1: Rearranging the equation, we get y = (-3/4)x^2 + (5/4)x + 1. This function is in the form of y = ax^2 + bx + c, where a = -3/4, b = 5/4, and c = 1. Therefore, function 3 is a quadratic function.
4. y = x - x^3: This function is not in the form of y = ax^2 + bx + c because it has an x^3 term. Therefore, function 4 is not a quadratic function.
In summary, the quadratic functions among the given functions are:
1. y = 2x^2 - 3x + 7
3. y = (5x - 3x^2)/4 + 1