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(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the vertex ,and x and y intercepts of the function
f%28x%29=-x%5E2%2B4x-3+
+f%28x%29=y
y=-x%5E2%2B4x-3 .... write in vertex form, complete square
y=-%28x%5E2-4x%2Bb%5E2%29-%28-1%2Ab%5E2%29-3 .....b=4%2F2=2
y=-%28x%5E2-4x%2B2%5E2%29%2B2%5E2-3+
y=-%28x-2%29%5E2%2B4-3+

y=-%28x-2%29%5E2%2B1+=> h=2 and k=1, so vertex is at (2,1)

x+intercepts :
set y=0
-x%5E2%2B4x-3+=0...factor
-x%5E2%2Bx%2B3x-3+=0
-%28x%5E2-x%29%2B%283x-3%29+=0
-x%28x-1%29%2B3%28x-1%29+=0
%283-x%29%28x-1%29+=0
x=3 or+x=1+
x intercepts are at (1,0) and (3,0)

y intercepts

set x=0
y=-0%5E2%2B4%2A0-3
y=+-3
y intercept is at (0,-3)


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2B4x-3%29+



Answer by MathTherapy(10557) About Me  (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 matrix%281%2C3%2C+x%2C+%22=%22%2C+-+b%2F%282a%29%29, or, where: 

The y-coordinate of the vertex is where 

Therefore, vertex, or matrix%281%2C5%2C+%22%28h%2C%22%2C+%22k%29%22%2C+%22=%22%2C+%22%282%2C%22%2C+%221%29%22%29

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: matrix%281%2C3%2C+0%2C+%22=%22%2C+-+x%5E2+%2B+3x+%2B+x+-+3%29 

                                                                             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(39630) About Me  (Show Source):
You can put this solution on YOUR website!
-1%28x%5E2-4x%2B3%29
-%28x-1%29%28x-3%29
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;
F%282%29=-%282-1%29%282-3%29=-%281%29%28-1%29=1
vertex is (2,1).

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