SOLUTION: please help me find the roots, lines of symmetry, and vertex for y=-x2+5x-4
Algebra.Com
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(75887) (Show Source): You can 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(16322) (Show Source): 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(20849) (Show Source): 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 :
RELATED QUESTIONS
Can someone please help me with this? Thanks
Graph the following equations and... (answered by stanbon)
Find the vertex of y = x2 + 5x + 4
(answered by lynnlo)
Please help me find the line of symmetry for the parabola: y= -(x - 2)^2 + 4 (answered by Alan3354)
For the graph of the function f (x) = x2 – 5x + 6, find the vertex and the axis of... (answered by ewatrrr,nerdybill)
please help me. i need help i cant figure this out.
if the roots of y = x2 + 10x +... (answered by solver91311)
Determine the vertex of the given equation. Parabolas.
y = -x2 + 5x - 6
Can you help me (answered by MathLover1)
{{{ (2/3)x^2-3x+6=y }}} I need to find the vertex and axis of symmetry to graph the... (answered by jim_thompson5910,Alan3354)
Find the vertex and the axis of symmetry for the parabola with the given equation.... (answered by stanbon)
y=5x^2-30x+47
Find the vertex and the axis of symmetry for the parabola with the given (answered by solver91311)