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

Question

Responses

y=−4x^2
y is equal to negative 4 x squared

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

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

y=8x
y is equal to 8 x

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

y=6x^2

Answer 1

To find the equations that represent parabolas, we need to identify equations of the form \( y = ax^2 + bx + c \), where \( a \) is not equal to zero. A parabola opens upwards or downwards depending on the sign of \( a \).

Let's evaluate each of the provided equations:

1. \( y = -4x^2 \)

   • This is a parabola that opens downward (since \( a = -4 < 0 \)).

2. \( y = 16x + 6 \)

   • This is a linear equation (not a parabola), as it can be written as \( y = 0x^2 + 16x + 6 \) (where \( a = 0 \)).

3. \( y = 2^x \)

   • This is an exponential equation (not a parabola).

4. \( y = 8x \)

   • This is also a linear equation (not a parabola), as it can be written as \( y = 0x^2 + 8x \) (where \( a = 0 \)).

5. \( y = (-9)^x \)

   • This is another exponential equation (not a parabola).

6. \( y = 6x^2 \)

   • This is a parabola that opens upward (since \( a = 6 > 0 \)).

Based on this analysis, the equations that represent a parabola are:

• \( y = -4x^2 \)
• \( y = 6x^2 \)

So, the responses that represent parabolas are:

• y = −4x^2
• y = 6x^2