SOLUTION: Find the vertex and Y and X intercepts of the function F(x)=-x^2+4x-3. is the F(x) considered they y? please and thank you

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Question 1183052: Find the vertex and Y and X intercepts of the function F(x)=-x^2+4x-3.
is the F(x) considered they y? please and thank you
Found 3 solutions by MathLover1, MathTherapy, josgarithmetic:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Find the vertex ,and and intercepts of the function


.... write in vertex form, complete square
.....



=> and , so vertex is at (,)

intercepts :
set
...factor




or
intercepts are at (,) and (,)

intercepts

set


intercept is at (,)






Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the vertex and Y and X intercepts of the function F(x)=-x^2+4x-3.
is the F(x) considered they y? please and thank you
It's NOT NECESSARY, at ALL, to complete the square, as the other person did, in order to get the vertex.

- x2 + 4x - 3

The x-coordinate of the vertex is where , or, where: 

The y-coordinate of the vertex is where 

Therefore, vertex, or 

For the y-intercept, substitute 0 for x, and solve for f(0), or y, as follows: 

                                                                             

For the x-intercepts, substitute 0 for f(x), or y, and solve for x, as follows: 

                                            Substituting 3x + x for 4x gives us:  

                                                                             0 = - x(x - 3) + 1(x - 3)

                                                                             0 = (- x + 1)(x - 3)

                                                                             0 = - x + 1     OR      0 = x - 3

                                                                             x = 1           OR      3 = x ====> x = 3                                                                               

                                                                               

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
 



x-intercepts are (1,0) and (3,0).





Vertex occurs in the exact middle of x at 1 and 3, which is for x=2;



vertex is  (2,1).





y-intercept, when x is 0, is at  (0,-3). 

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