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9. Intercept of a function example ( Enter your problem )
  1. y=x2+3x-4 Example-1
  2. y=(x+2)2-9 Example-2
  3. y=3x2+6x-1 Example-3
  4. y=3(x+1)2-4 Example-4
Other related methods
  1. Domain of a function
  2. Range of a function
  3. Inverse of a function
  4. Properties of a function
  5. Parabola Vertex of a function
  6. Parabola focus
  7. axis symmetry of a parabola
  8. Parabola Directrix
  9. Intercept of a function
  10. Parity of a function
  11. Asymptotes of a function

2. y=(x+2)2-9 Example-2
(Previous example)
4. y=3(x+1)2-4 Example-4
(Next example)

3. y=3x2+6x-1 Example-3





y=3x2+6x-1, find Intercept of a function

Solution:
y=3x2+6x-1

1. 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=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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2. y=(x+2)^2-9 Example-2
(Previous example)
4. y=3(x+1)^2-4 Example-4
(Next example)





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