y=3x2+6x-1, find Intercept of a functionSolution:y=3x2+6x-11. Intercepts : Intercept :
To find the y-intercept put x=0 in
y=3x2+6x-1, we get
y=3(0)2+6(0)-1=-1:. y-intercept is
(0,-1)To find the x-intercept put y=0 in
y=3x^2+6x-1, we get
=>3x^2+6x-1=0factor is not possible for equation
3x^2+6x-1=0But we are trying find solution using the method of perfect square.
Comparing the given equation with the standard quadratic equation
ax^2+bx+c=0,we get,
a=3, b=6, c=-1.:. Delta=b^2-4ac=(6)^2-4 (3) (-1)=36+12=48:. sqrt(Delta)=sqrt(48)=4sqrt(3)Now,
alpha=(-b+sqrt(Delta))/(2a)=(-(6)+4sqrt(3))/(2*3)=(-6+4sqrt(3))/6=(-3+2sqrt(3))/3 and,
beta=(-b-sqrt(Delta))/(2a)=(-(6)-4sqrt(3))/(2*3)=(-6-4sqrt(3))/6=(-3-2sqrt(3))/3=>x = (-3+2sqrt(3))/3" or "x = (-3-2sqrt(3))/3:. x-intercepts are
((-3+2sqrt(3))/3,0) and
((-3-2sqrt(3))/3,0):. x-intercepts are
(0.1547,0) and
(-2.1547,0)
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then