How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x) = -7x^2 + 3x + 1#?
The function is a quadratic equation; and we know that the graph is a parabola:
Since the coefficient of a is negative 7, the parabola will reflect about the x-axis (to give smth like a frowny face, if that helps you to memorise). This also explains why the graph has a maximum point.
Since c, which equals to the y-intercept, is 1, the graph will intersect the y axis at (0,1)
In order to find the axis of symmetry (and the coordinates of the maximum point of this function), simply express the equation in the standard form. it will give the coordinates of the vertex, (h,k) and the axis of symmetry will occur at x = h