Question

Which of the following parabolas would open downwards?(1 point)
Responses

y=(x−5)2−4
y is equal to open paren x minus 5 close paren squared minus 4

y=8(x−1)2+2
y is equal to 8 times open paren x minus 1 close paren squared plus 2

y=4(x+6)2−3
y is equal to 4 times open paren x plus 6 close paren squared minus 3

y=−3(x+4)2+9
y is equal to negative 3 times open paren x plus 4 close paren squared plus 9

Answer 1

A parabola opens downwards if the coefficient of the squared term is negative.

Let's analyze the given equations:

1. **\( y = (x - 5)^2 - 4 \)**: The coefficient of the squared term is \( +1 \) (positive), so this parabola opens upwards.

2. **\( y = 8(x - 1)^2 + 2 \)**: The coefficient of the squared term is \( +8 \) (positive), so this parabola opens upwards.

3. **\( y = 4(x + 6)^2 - 3 \)**: The coefficient of the squared term is \( +4 \) (positive), so this parabola opens upwards.

4. **\( y = -3(x + 4)^2 + 9 \)**: The coefficient of the squared term is \( -3 \) (negative), so this parabola opens downwards.

Therefore, the parabola that opens downwards is:

**\( y = -3(x + 4)^2 + 9 \)**.