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

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

y=8(x−1)2+2

Answer 1

To determine which of the given parabolas opens downwards, we need to look at the coefficient of the squared term in each equation. Specifically, if the coefficient (the number in front of the \((x - a)^2\) term) is negative, the parabola opens downwards.

Let's analyze the given equations:

1. \(y = (x - 5)^2 - 4\)

Coefficient of \((x - 5)^2\) is \(1\) (positive). **Opens upwards.**

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

Coefficient of \((x + 4)^2\) is \(-3\) (negative). **Opens downwards.**

3. \(y = 4(x + 6)^2 - 3\)

Coefficient of \((x + 6)^2\) is \(4\) (positive). **Opens upwards.**

4. \(y = 8(x - 1)^2 + 2\)

Coefficient of \((x - 1)^2\) is \(8\) (positive). **Opens upwards.**

From this analysis, the only parabola that opens downwards is:

**y = -3(x + 4)² + 9.**