Question

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

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

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

y=8x
𝑦
=
8
𝑥
y is equal to 8 x

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

y=−4x2
𝑦
=
−
4
𝑥
2
y is equal to negative 4 x squared

y=6x2
𝑦
=
6
𝑥
2
y is equal to 6 x squared

Answer 1

To determine which equations will form a parabola when graphed, we need to identify the equations that are quadratic in form (typically written as \(y = ax^2 + bx + c\)), where \(a\), \(b\), and \(c\) are constants.

Let's analyze the options given:

1. **\(y = (-9)x\)**: This is a linear equation. It will result in a straight line, not a parabola.
2. **\(y = 2^x\)**: This is an exponential equation. It will not be a parabola.
3. **\(y = 8x\)**: This is also a linear equation. It will result in a straight line, not a parabola.
4. **\(y = 16x + 6\)**: This is a linear equation. It forms a straight line, not a parabola.
5. **\(y = -4x^2\)**: This is a quadratic equation. It will graph as a parabola that opens downward.
6. **\(y = 6x^2\)**: This is also a quadratic equation. It will graph as a parabola that opens upward.

**Final selections:**
- \(y = -4x^2\)
- \(y = 6x^2\)

These two equations (5 and 6) will form parabolas when graphed.