Question

Select all the equations which, when graphed, will be a parabola.(2 points)
Responses

y=(−9)x
y is equal to negative 9 to the x th power

y=−4x2
y is equal to negative 4 x squared

y=8x
y is equal to 8 x

y=6x2
y is equal to 6 x squared

y=16x+6
y is equal to 16 x plus 6

y=2x
y is equal to 2 to the x th power

Answer 1

To determine which equations will form a parabola when graphed, we should look for equations that can be expressed in the standard form of a quadratic equation, which is:

\[ y = ax^2 + bx + c \]

Equations that contain \(x^2\) as the highest degree term will graph as parabolas.

Now let's analyze the provided equations:

1. **y = (−9)x**: This is a linear equation (first degree) and will not graph as a parabola.

2. **y = −4x²**: This is a quadratic equation. It has \(x^2\) as the highest degree term and will graph as a parabola.

3. **y = 8x**: This is also a linear equation (first degree) and will not graph as a parabola.

4. **y = 6x²**: This is a quadratic equation. It also has \(x^2\) as the highest degree term and will graph as a parabola.

5. **y = 16x + 6**: This is a linear equation (first degree) and will not graph as a parabola.

6. **y = 2^x**: This is an exponential function, not a polynomial, and will not graph as a parabola.

Based on this analysis, the equations that will form a parabola when graphed are:

- **y = −4x²**
- **y = 6x²**