Question

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

y=6x^2
y is equal to 6 x squared

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

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

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

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

y=8x

Answer 1

The equations that, when graphed, will form a parabola are those that can be expressed in the form of \( y = ax^2 + bx + c \), where \( a \) is not equal to zero.

From your list, the equations that are parabolas are:

1. \( y = 6x^2 \) (which is a quadratic equation with \( a = 6 \))
2. \( y = -4x^2 \) (which is a quadratic equation with \( a = -4 \))

The other equations do not represent parabolas:

- \( y = 2^x \) is an exponential function.
- \( y = 16x + 6 \) is a linear equation.
- \( y = (-9)^x \) is an exponential function.
- \( y = 8x \) is a linear equation.

So, the correct responses are:

- \( y = 6x^2 \)
- \( y = -4x^2 \)