Question
Select all the equations which, when graphed, will be a parabola.(2 points) Responses y=16x+6 y is equal to 16 x plus 6 y=6x2 y is equal to 6 x squared y=(−9)x y is equal to negative 9 to the x th power y=2x y is equal to 2 to the x th power y=8x y is equal to 8 x y=−4x2 y is equal to negative 4 x squared
Answers
GPT-4o mini
In order to determine which equations graph as parabolas, we will identify the equations based on their forms. A parabola can be represented generally as \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, and \(a \neq 0\).
Now, let's analyze the given equations:
1. \(y = 16x + 6\) - This is a linear equation (not a parabola).
2. \(y = 6x^2\) - This is a parabolic equation (it has the \(x^2\) term).
3. \(y = (-9)x\) - This is a linear equation (not a parabola).
4. \(y = 2^x\) - This is an exponential equation (not a parabola).
5. \(y = 8x\) - This is a linear equation (not a parabola).
6. \(y = -4x^2\) - This is a parabolic equation (it has the \(x^2\) term).
The equations that will graph as parabolas are:
- \(y = 6x^2\)
- \(y = -4x^2\)
So the final selections for the equations that graph as parabolas are:
- \(y = 6x^2\)
- \(y = -4x^2\)
Now, let's analyze the given equations:
1. \(y = 16x + 6\) - This is a linear equation (not a parabola).
2. \(y = 6x^2\) - This is a parabolic equation (it has the \(x^2\) term).
3. \(y = (-9)x\) - This is a linear equation (not a parabola).
4. \(y = 2^x\) - This is an exponential equation (not a parabola).
5. \(y = 8x\) - This is a linear equation (not a parabola).
6. \(y = -4x^2\) - This is a parabolic equation (it has the \(x^2\) term).
The equations that will graph as parabolas are:
- \(y = 6x^2\)
- \(y = -4x^2\)
So the final selections for the equations that graph as parabolas are:
- \(y = 6x^2\)
- \(y = -4x^2\)