Question

For the equation

?f(x)equals=x squared minus 2 x minus 15x2?2x?15?,

?a) determine whether the graph of the given quadratic function opens up or? down, ?b) find the? vertex, ?c) find the axis of? symmetry, ?d) find the? x- and? y-intercepts, and ?e) sketch the graph of the function.

Answer 1

(a). We have ?f(x) = x²?2x?15?. Since the coefficient of the leading term, i.e. x² , is positive, the quadratic function (parabola) will open upwards.

(b). f(x) = x²?2x?15 = x²?2x+1 -16 = (x-1)² -16. This is the vertex form of the given quadratic function (parabola) . Its vertex is at the point (1,-16).

(c ). The axis of symmetry is the line parallel to the Y-Axis, which passes through the vertex, i.e. the line x = 1.

(d). The x- intercept is where y = 0, i.e. where x²?2x?15 = 0 or, x²?5x+3x?15 = 0 or, x(x-5)+3(x-5) = 0 or, (x+3)(x-5) = 0. Thus, x = -3 and x = 5 are the 2 x-intercepts. The y- intercept is where x = 0. Thus, the y- intercept is y = -15.

e). A graph of the function is attached.