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x^2-4x+5 = - x^2+4x-1
Let's solve this equation by using the Quadratic Formula. Before we can do that though, we must move all terms to one side of the equation.
Now we can solve the equation using the Quadratic formula.
Use the Quadratic Formula: a = 1, b= -4, c= 3
- (- a)=a
Calculate power and product
Subtract term
Calculate root
Calculate quotient
State solutions
(I), (II): Add and subtract terms
The system has two solutions, one at x=1 and another at x=3. This means the functions intersect twice. By substituting these values into either equation, we can calculate the corresponding y-values. y= 1^2-4( 1)+5 ⇔ y=2 y= 3^2-4( 3)+5 ⇔ y=2 The system has two points of intersection, (1,2) and (3,2).
As we can see, we did not need to use the Quadratic Formula to solve the equation. The system has a solution in x=-1. By substituting this value into either equation, we can calculate the corresponding y-value. y=( -1)^2-( -1)-2 ⇔ y=0 The system has a point of intersection at (-1,0).
