Identity, <span>For example, x + x = 2x is </span>true for every value<span> of x.</span>
Answer: 3
Step-by-step explanation:
Answer:
![\large\boxed{f(x)=(x+1)^2-4}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bf%28x%29%3D%28x%2B1%29%5E2-4%7D)
Step-by-step explanation:
![\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================](https://tex.z-dn.net/?f=%5Ctext%7BThe%20vertex%20form%20of%20a%20quadratic%20equation%7D%5C%20f%28x%29%3Dax%5E2%2Bbx%2Bc%3A%5C%5C%5C%5Cf%28x%29%3Da%28x-h%29%5E2%2Bk%5C%5C%5C%5C%28h%2C%5C%20k%29-%5Ctext%7Bvertex%7D%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================](https://tex.z-dn.net/?f=%5Cbold%7BMETHOD%5C%201%3A%7D%5C%5C%5C%5C%5Ctext%7Bconvert%20to%20the%20perfect%20square%7D%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5Cqquad%28%2A%29%5C%5C%5C%5Cf%28x%29%3Dx%5E2%2B2x-3%3D%5Cunderbrace%7Bx%5E2%2B2%28x%29%281%29%2B1%5E2%7D_%7B%28%2A%29%7D-1%5E2-3%5C%5C%5C%5Cf%28x%29%3D%28x%2B1%29%5E2-4%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4](https://tex.z-dn.net/?f=%5Cbold%7BMETHOD%5C%202%3A%7D%5C%5C%5C%5C%5Ctext%7BUse%20the%20formulas%3A%7D%5C%20h%3D%5Cdfrac%7B-b%7D%7B2a%7D%2C%5C%20k%3Df%28k%29%5C%5C%5C%5Cf%28x%29%3Dx%5E2%2B2x-3%5Cto%20a%3D1%2C%5C%20b%3D2%2C%5C%20c%3D-3%5C%5C%5C%5Ch%3D%5Cdfrac%7B-2%7D%7B2%281%29%7D%3D%5Cdfrac%7B-2%7D%7B2%7D%3D-1%5C%5C%5C%5Ck%3Df%28-1%29%3D%28-1%29%5E2%2B2%28-1%29-3%3D1-2-3%3D-4%5C%5C%5C%5Cf%28x%29%3D%28x-%28-1%29%29%5E2-4%3D%28x%2B1%29%5E2-4)
Answer:
x = 2
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(4+(4•(x-2)))-(2•(x+1)-x) = 0
Step 2 :
Equation at the end of step 2 :
(4 + 4 • (x - 2)) - (x + 2) = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
3x - 6 = 3 • (x - 2)
Equation at the end of step 4 :
3 • (x - 2) = 0
Step 5 :
Equations which are never true :
5.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
5.2 Solve : x-2 = 0
Add 2 to both sides of the equation :
x = 2
One solution was found :
x = 2
Processing ends successfully
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Answer:
Is their an equation that can be used a reference to find the sum/difference/product/quotient to this equation?
Step-by-step explanation: