In order to solve this, we have to identify the function represented by each graph and its tranformations. The first graph is a parabola, this kind of functions are represented by an equation of the form:
f(x) = x²
This equation represents the simplest parabola, when we want the parabola to open downwards the coefficientof of the x² term must be a negative number, then we rewrite the equation like this so it opens downward:
f(x) = -x²
If we want the parabola to translate vertically some units we must add the units we want to move the graph, in this case, we want to move the graph 2 units up, then we can rewrite the above equation to get:
f(x) = -x² + 2
Then, the first graph is represented by the function f(x) = -x² + 2.
Fo the second graph, we have a parabola that opens upward, then the equation of the graph would have an equation of the form f(x) = x², if we want the graph to move some units to the right we must subtract the units we want the graph to move from the variable x, in this case, we want the parabola to move 2 units to the right, then we have to rewrite the equation to get:
f(x) = (x - 2)²
The third graph looks like the graph of an absolute value function of the form f(x) = |x|, like the parabola, if we want the absolute value function to open downward the coeficient of the |x| term must be a negative value, thenwe get:
f(x) = -|x|
And in order to translate the graph some units left we must add them to the variable x, since we want to move the graph 2 units left we would have to rewrite the function like this:
f(x) = -|x + 2|
For the last graph, we can notice that it has the form of an absolute value function, opening downward and translated 2 units up, then we can write its equation like this:
f(x) = -|x| + 2
Summary:
Match the gaphs and the functions like this:
