Question

After you find the vertex of the parabola f(x)=-2(x+1)^2+7does it open up or down?

Answer 1

The given equation is:

`f(x)=-2(x+1)^2+\text{ 7}`

The equation of a parabola can be expressed in vertex form as:

`\begin{gathered} f(x)=a(x-h)^2+\text{ k} \\ \text{Where }the\text{ coordinates of the vertex are (h, k)} \end{gathered}`

Comparing this formula with then function given:

a = -2

h = -1

k = 7

The vertex = (h, k)

Vertex = ( -1, 7)

Note that:

If in a parabola, the x is squared, the parabola either opens up or down

If the multiplier, a, is positive, then it is certain that the parabola opens up

If the multiplier is negative, then the parabola opens down.

In the equation of the parabola given, that is, f(x)=-2(x+1)²+7:

a = -2 (negative), then the parabola opens down.