Without graphing, describe the end behavior of the graph of f(x)= -5x^2-3x+1
as x starts from a negative value and increases the equation -5x^2-3x+1 curves up and peaks and comes down and passes the y-intercept at (0,1) to negative infinity.
I don't know what the answer is. I got it wrong, I would love some el helpo
To determine the end behavior of a polynomial function without graphing, we look at the leading term of the function. The leading term is the term with the highest power of x.
In the given function f(x) = -5x^2 - 3x + 1, the leading term is -5x^2. The degree of this term is 2, which is an even number.
For even degree polynomials, the end behavior can be described as follows:
1. If the leading coefficient (the coefficient of the leading term) is positive, then the graph opens upwards on both ends and approaches positive infinity as x goes to both positive and negative infinity.
2. If the leading coefficient is negative, then the graph opens downwards on both ends and approaches negative infinity as x goes to both positive and negative infinity.
In our case, since the leading coefficient is -5 (which is negative), the graph of f(x) = -5x^2 - 3x + 1 will open downwards on both ends and approach negative infinity as x goes to both positive and negative infinity.
So, to summarize, as x starts from a negative value and increases, the graph of f(x) curves downward, reaches a peak, and approaches negative infinity. It passes through the y-intercept at (0,1) and continues downward indefinitely.