Question

Creat an equation for a cubic function, in standard form, that has x- intercept given by the set {-3,1,7} and which passes through the points (-2,54)

Answer 1

Given :

Set of x-intercepts {-3,1,7},

point through which it passes (-2,54)

Now,

Step 1: Substitute value of x intercepts in equation, $y=a(x-p)(x-q)(x-r)$, we get,

$y=a(x-(-3))(x-1)(x-7)$

$y= a(x+3)(x-1)(x-7)$               ... equation (1)

Step 2: substitute x an y with the point through which it passes,

$54=a((-2)+3)((-2)-1)((-2)-7)$

$54 = 27a$

∴ $a=2$

Step 3: Now, substituting value of a in equation (1), we have

$y=(2x+6)(x^{2} -8x+7)$

$y=2x^{3}-10x^{2} -34x +42$   (Requited cubic equation)