Answer:
![\boxed{\boxed{B.\ f(x)=\dfrac{3}{4}x^2+2x-5}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7BB.%5C%20f%28x%29%3D%5Cdfrac%7B3%7D%7B4%7Dx%5E2%2B2x-5%7D%7D)
Step-by-step explanation:
Quadratic function-
It is a function that can be represented by an equation of the form
, where
In a quadratic function, the greatest power of the variable is 2.
As in the first option the highest power is 3, so it is not a quadratic function.
Even though the power of x is 2 in the third option, but as it is in the denominator, so the overall power of x becomes -2. Hence it is not a quadratic function.
As the coefficient of
is 0 in case of fourth option, so it is not a quadratic function.
Equation in option 2 satisfies all the conditions of quadratic function, hence it is the quadratic function.
Let's solve this by using the quadratic formula:
![\frac{-b+-\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
Note that we only use the coefficients so a=12, b=-14, and c=-6.
Plug values in the quadratic equation:
![\frac{ - ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%20%20%28%20-%2014%29%C2%B1%20%5Csqrt%7B%20%7B%28%20-%2014%29%7D%5E%7B2%7D%20-%204%2812%29%28%20-%206%29%20%7D%20%7D%7B2%2812%29%7D%20)
And so by evaluating those values we obtain:
![\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7B14%2B-%5Csqrt%7B484%7D%20%7D%7B24%7D%3D%5Cfrac%7B14%2B-22%7D%7B24%7D%20%20%5C%5C%5C%5C)
Now we have two answers which are our factors one where we add another where we subtract and so:
First factor:
![\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B14%2B22%7D%7B24%7D%3D%5Cfrac%7B36%7D%7B24%7D%3D%5Cfrac%7B3%7D%7B2%7D)
Second Factor:
![\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B14-22%7D%7B24%7D%3D%5Cfrac%7B-8%7D%7B24%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
And so your factors are
![\frac{3}{2},-\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%2C-%5Cfrac%7B1%7D%7B3%7D)
meaning that those are your roots/x-intercepts.
Answer:
29,892
Step-by-step explanation:
811,968-782,076
It is C
Step-by-step explanation:
Because if you take into consideration that pn is equal to 10 and mn is equal to 5 and nq is equal to 8 then you add all them up which gives you 23 then subtract 14, and you get 9
Hope this helped you