Question

Select the true statement for the graph of f(x)=a(x+5)ˆ2-2, where a<0

 

minimum is 5

minimum is -2

max is 5

min is -5

max is -5

max is -2

Answer 1

The parabola equation f(x) = a(x + 5)² - 2

y = a[x - (- 5)]² - 2

Compare it to vertex form of parabola y = a(x - h)² - k

(h, k) = (- 5, -2)

Vertex is the minimum or maximum point of parabola.

When a  is positive number the parabola opens up and has minimum value.

When a  is negative number the parabola opens down and has maximum value.

In this case a < 0

So it was downward parabola.

In the maximum point h  = -5 and k = - 2  so the graph of parabola cannot be upper than  -2.

The maximum value of y = - 2 occurs at x = -5.

The maximum is - 2 .

Last option is correct.