Ask a New Question
Menu

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

1 answer

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