Graph the function g(x) = 2(x - 2)^2 + 2
1 answer:
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In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say
So required equation is
![= a[(x^2 - 2x - 3x + 6)(x-5)]](https://tex.z-dn.net/?f=%3D%20a%5B%28x%5E2%20-%202x%20-%203x%20%2B%206%29%28x-5%29%5D)
![= a[(x^2 - 5x+6)(x-5)]](https://tex.z-dn.net/?f=%3D%20a%5B%28x%5E2%20-%205x%2B6%29%28x-5%29%5D)
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
So required equation of cubic polynomial is
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
So we will let specific cubic polynomial function of the form
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say
So required equation is
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
So required equation of cubic polynomial is
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.