Answer
(a)
$a = 1: f(x) = (x + 5)(x - 3) = x^2 + 2x - 15$
$a = 2: f(x) = 2(x + 5)(x - 3) = 2x^2 + 4x - 30$
$a = - 2: f(x) = -2(x + 5)(x - 3) = -2x^2 - 4x + 30$
$a = 5: f(x) = 5(x + 5)(x - 3) = 5x^2 + 10x - 75$
Work Step by Step
(a)
$a = 1: f(x) = (x + 5)(x - 3) = x^2 + 2x - 15$
$a = 2: f(x) = 2(x + 5)(x - 3) = 2x^2 + 4x - 30$
$a = - 2: f(x) = -2(x + 5)(x - 3) = -2x^2 - 4x + 30$
$a = 5: f(x) = 5(x + 5)(x - 3) = 5x^2 + 10x - 75$
(b) The value of a does not affect the x-intercepts, but it changes the y-intercept by a factor of a.
(c) The value of a does not affect the axis of symmetry. It is $x = - 1$ for all values of a.
(d) The value of a does not affect the x-coordinate of the vertex. However, the y-coordinate of the vertex is multiplied by a.
(e) The mean of the x-intercepts is the x-coordinate of the vertex.