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SOLUTION: please help me find the roots, lines of symmetry, and vertex for y=-x2+5x-4
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Question 414468
:
please help me find the roots, lines of symmetry, and vertex for y=-x2+5x-4
Found 3 solutions by
stanbon, rfer, MathLover1
:
Answer by
stanbon(69061)
(
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):
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put this solution on YOUR website!
please help me find the roots, lines of symmetry, and vertex for
y=-x^2+5x-4
----
-x^2+5x+? = y+4+?
----
Complete the square on the x-terms:
-(x^2-5+(5/2)^2) = y+4-(5/2)^2
---
Factor:
-(x-(5/2))^2 = y + 16/4 - (25/4)
----
-(x-(5/2))^2 = y -9/4
-------
Symmetry line : x = 5/2
Vertex: (5/2 , (9/4))
----
Roots of y = -x^2+5x-4
Solve -x^2+5x-4 = 0
x^2-5x+4 = 0
(x-4)(x-1) = 0
x = 1 or x = 4
---
Cheers,
Stan H.
Answer by
rfer(15570)
(
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):
You can
put this solution on YOUR website!
zero's =(1,0), (4,0)
vertex=(2.5,2.5)
axis=2.5
Answer by
MathLover1(11324)
(
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):
You can
put this solution on YOUR website!
....factor
This is a quadratic equation (degree of 2), so
First, find x-intercepts,
Let
and solve for
:
........->....
and
........->....
So, the
(roots) are (4,0) and (1,0)
Now, find the
, let
and solve for
,
, so the
is (0,-4)
The axis of
is just the average of the two
,
So, the axis of symmetry is
Since the sign of
is negative then this function will have a maximum.
Now, to find it's maximum (vertex).
Formula for maximum value is
,
,
( Coefficients of
)
this is exactly
, which is not surprising because the
on the axis of
.
Now, find the
value corresponding to the
value,
Substitute,
into the equation and solve for
,
Summarize:
You should have more than enough now for a graph,
: (4,0) and (1,0)
: (0,-4)
maximum value (vertex) : (2.5,2.25)
axis of
: