These are some general characteristics that describe the graph of the quadratic function f(x)=3x^2 −x+15.
The given function is a quadratic function f(x)=3x^2 −x+15, and quadratic functions generally represent a parabolic graph. Here are some words that describe the graph of this quadratic function:
Concave Upward: The coefficient of the x^2 term is positive (3 in this case), indicating that the parabola opens upward.
Vertex: The vertex of the parabola can be found using the formula
−b/ 2a
where a is the coefficient of x^2 , and b is the coefficient of x. In this case, the vertex would be ( 1/6 , 227/2 ).
Minimum Value: Since the parabola opens upward, it has a minimum value at its vertex.
Axis of Symmetry: The axis of symmetry for this parabola is the vertical line passing through its vertex.
Intercepts: You can find the x-intercepts by setting f(x) equal to zero and solving for x. Similarly, the y-intercept is the value of f(x) when x=0.
Positive Leading Coefficient: The leading coefficient (coefficient of x^2 ) is positive, indicating that the graph is upward-sloping.
These are some general characteristics that describe the graph of the quadratic function f(x)=3x^2 −x+15.