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Find the vertex and axis of symmetry of the quadratic y=x^2-5x+6
Please Help with Math. Will give 5 stars to whomever answers?
2016-01-02 6:39 pm
回答 (6)
2016-01-02 6:46 pm
✔ 最佳答案
y = x^2 - 5x + 6Factor:
y = (x - 6)(x + 1)
y = 0 when x = -1 or 6.
Therefore the axis of symmetry is between x = -1 and 6.
So the axis of symmetry is the line x = 5/2.
The vertex is the point on the curve and on the axis of symmetry so plug in 5/2 to the equation of the curve.
y = (5/2)^2 - 5(5/2) + 6
y = (25/4) - (25/2) + 6
y = -1/4
Answers:
Axis of Symmetry: x = 5/2
Vertex: (5/2, -1/4)
2016-01-02 6:40 pm
Look up the Common Core, coz my answer will likely get you a failing grade.
2016-01-02 8:31 pm
y = [ x² - 5x + 25/4 ] - 25/4 + 6
y = [ x - 5/2 ]² - 1/4
Vertex (5/2 , - 1/4)
Axis of symmetry is x = 5/2
y = [ x - 5/2 ]² - 1/4
Vertex (5/2 , - 1/4)
Axis of symmetry is x = 5/2
2016-01-02 7:55 pm
if you convert the equation to vertex by completing the square
x^2 - 5x + 6 = y
x^2 - 5x + (5/2)^2 + 6 - (5/2)^2 = y
x^2 - 5x + 25/4 + 6 - 25/4 = y
(x - 5/2)^2 - 1/4 = y
y = (x - h)^2 + k
where h, k is the vertex
h = 5/2
k = -1/4
(5/2, -1/4) is the vertex
x = 5/2 is the axis of symmetry
x^2 - 5x + 6 = y
x^2 - 5x + (5/2)^2 + 6 - (5/2)^2 = y
x^2 - 5x + 25/4 + 6 - 25/4 = y
(x - 5/2)^2 - 1/4 = y
y = (x - h)^2 + k
where h, k is the vertex
h = 5/2
k = -1/4
(5/2, -1/4) is the vertex
x = 5/2 is the axis of symmetry
2016-01-02 7:22 pm
Axis of symmetry: x=2.5
Vertex = (2.5,-.25)
Also written as (5/2, -1/4)
Vertex = (2.5,-.25)
Also written as (5/2, -1/4)
2016-01-02 6:45 pm
The vertex is found by taking the first derivative and determining the value of x for which y is a minimum.
The axis of symmetry is x=a where a is the value of x that minimises y.
Another approach without calculus is to factorise the quadratic to find the two roots. The value of a is the arithmetic mean of these two roots.
The axis of symmetry is x=a where a is the value of x that minimises y.
Another approach without calculus is to factorise the quadratic to find the two roots. The value of a is the arithmetic mean of these two roots.
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