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Vertex of the Parabola - Apllied Math

by preet
(canada)










































Sketch Y = X² -6X + 5. Find and label the vertex of the parabola.

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Feb 26, 2012
Vertex of the Parabola
by: Staff

Question:

Sketch Y = X² - 6X + 5. Find and label the vertex of the parabola.


Answer:


y = x² - 6x + 5

the general form of a parabola is:

y = ax² + bx + x

the quadratic formula is:

x = (-b/2a) ± [√(b² - 4ac)/2a]

the x coordinate of the vertex of the parabola is:

x_vertex = (-b/2a)

for your equation:

a = 1

b = -6

x_vertex = -(-6)/(2*1)

x_vertex = 6/2

x_vertex = 3


now that you know the x coordinate of the vertex, substitute this value in the original equation to compute y

y = x² - 6x + 5

x = 3

y = 3² - 6*3 + 5

y = 9 - 18 + 5

y = -4


the coordinates of the vertex in x,y format are: (3, -4)


You can also compute the vertex by rewriting the equation as follows:

y = x² - 6x + 5

y = (x² - 6x) + 5

y = [x² - 2*(-3x) + 9 - 9] + 5

y = (x - 3)² - 9 + 5

y = (x - 3)² - 4

As you can see, the vertex is (3, -4)



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Thanks for writing.

Staff
www.solving-math-problems.com



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