SOLUTION: What is the domain of f, range of f, vertex, axis of symmetry, x-intercept (s), y-intercept, determine whether it has a minimum or a maximum value and state that value for f(x)=x^2
Question 190301: What is the domain of f, range of f, vertex, axis of symmetry, x-intercept (s), y-intercept, determine whether it has a minimum or a maximum value and state that value for f(x)=x^2+x-2
PLZZZZ help me in STRUGGLING! Answer by solver91311(24713) (Show Source):
Since there are no real number values for which this function is undefined the domain is all real numbers or .
Since this is a quadratic polynomial, the graph is a parabola. Since the lead coefficient is positive, the parabola opens upward. Let's table discussion of the Range until we have identified the vertex.
The x-coordinate of the vertex of a parabola described by a function in the form:
is given by:
so for your function:
The y-coordinate of the vertex of such a parabola is given by
So the vertex is the point
Since this is a parabola opening upward, the y-coordinate of the vertex represents the minimum value of the function. And there is no maximum value, so we can now define the range as [,). This also answers the question about whether there is a minimum or maximum -- and what the value of the minimum is.
The axis of symmetry is the vertical line defined by the equation where a is the value of the x-coordinate of the vertex, so:
The y-intercept is the value of the function when x equals zero, so:
The x-intercepts are the values of x that make the value of the function equal zero, so:
