`y=3x^2+6x-1`, find Intercept of a function
Solution:
`y=3x^2+6x-1`
1. Intercepts :
Intercept :
To find the y-intercept put x=0 in `y=3x^2+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=0`
factor is not possible for equation `3x^2+6x-1=0`
But 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.
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