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

Question

Responses

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

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

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

y=4(x+6)2−3

Answer 1

A parabola opens downwards if the coefficient of the squared term (the "a" value in the standard form \( y = a(x - h)^2 + k \)) is negative.

Let's analyze each given equation:

1. \( y = -3(x + 4)^2 + 9 \)
   Coefficient of \((x + 4)^2\) is -3 (negative) → Opens downward.

2. \( y = 8(x - 1)^2 + 2 \)
   Coefficient of \((x - 1)^2\) is 8 (positive) → Opens upward.

3. \( y = (x - 5)^2 - 4 \)
   Coefficient of \((x - 5)^2\) is 1 (positive) → Opens upward.

4. \( y = 4(x + 6)^2 - 3 \)
   Coefficient of \((x + 6)^2\) is 4 (positive) → Opens upward.

The only parabola that opens downwards is:

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