Parabolas and y intercepts

Question

In the equation y=-2(x+1)²-4 it asks to determine whether the graph opens upward or downward, and also the pattern of change in the y values, i am confused as to how you are suppose to find the pattern of change in the y values?

Answer 1

Ton understand this kind of problem, start with the basics....

Consider the equation y = x² :

Plot the values of y for x = 0, +1, -1, +2, and -2. You will see the typical parabola shape---opening up.

Now do the same thing for y = - x² Now the curve opens down.

Plot your given equation to see how it compares to the second example.

Answer 2

My guess is they are referring to how y changes as x changes. So the answer is just the equation itself and/or the graph of the quadratic.

Answer 3

y=a(x-h)^2+k is the vertex form of the parabola

y=-2(x+1)^2-4

the following all happens to the parent function y=x^2

the "-" sign in front of the 2 means that the parabola is reflected over the x-axis; that is, the parabola opens downward

the 2 means a vertical stretch by a factor of 2

the +1 means a translation 1 unit horizontally left (1=-[-1], that is, h=-1)

the -4 means a translation 4 units vertically down

graph y=x^2 and graph this function, compare the graphs, and you will see these transformations