The fourth graph represents the function.
We have to rewrite the given function into the standard form of a parabola.
What is a parabola?
A parabola is a U-shaped plane curve that is symmetrical about its vertex.
What is the standard form of a parabola?
The standard form of a parabola is given by:
y = (x-h)²+k
Where (h,k) is the vertex of the parabola.
- The given function is rewritten in its standard form:
f(x) = x²+2x-1
We can rewrite this as:
f(x) = x²+2x+1-2
f(x) =( x+1)²-2
- By observing the function in standard form, we can see that the vertex of the parabola is (-1,-2).
Now compare this with the given graphs. The only graph that has its vertex at (-1,-2) is the fourth graph.
We have found the graph that represents the function f(x) = x²+2x-1 to be the fourth graph.
Learn more about parabolas here-https://brainly.com/question/16000692
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