x^2 - 2x + 5 in vertex form?
X^2+ 6x - 2 in vertex form?
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- 3+ months ago by demitiafr...
- Topics:
- form, homework, math, algebra
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Answers (2)
First you need to learn correct presentation. You can not stand spelling mistrakes in math. X is not x and a math program will not tell you that you made a mistake, it will just give you goofy results. Without an equal sign, you don't have a question. There is no answer when you don't know what the question is.
So let's assume you meant y = x^2 + 6x - 2. That is the equation of a parabola, and all named equations are completely explained at wikipedia.org
[quote
The equation can be generalized to allow the vertex to be at a point other than the origin by defining the vertex as the point (h, k). The equation of a parabola with a vertical axis then becomes
( x − h )^2 = 4p(y − k )
The last equation can be rewritten
y = ax^2 + bx + c
so the graph of any function which is a polynomial of degree 2 in x is a parabola with a vertical axis.
endquote]
Other sections of that site explain how to find the values of h and k directly.
y = x² + 6x - 2 , a parabola in standard form generally expressed as:
y = ax² + bx + c , with a=1, b=6, c= -2 in this instance.
The vertex form of a parabola's equation is generally expressed as: y = a(x - h)² + k,
where h gives you the x-coordinate and k gives you the y-coordinate of the parabola's vertex. In order to obtain thie vertex form from the standard form, you have to factor the latter and to complete the square. In the example this means:
y = (x + 3)² -11.
If you expand this, you get:
y = x² + 6x + 9
but as it says -2 and not +9 you have to add -11 to get it right.
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y = x² - 2x + 5
in vertex form:
y = (x - 1)² + 4.
If you are uncomfortable with the above mentioned method, you can use another relation:
Based on the standard form y = ax² + bx + c you can find the axis of symmetry of the parabola in question, thereby getting the x-value of the vertex:
x = - b/(2a)
Then inserting this x-value into the parabola's standard form, yields the y-value of the vertex. Let's do it:
x = - (-2/(2*1)) = 1 and
f(1) = 1 - 2 + 5 = 4.
Wrapping the rest of the vertex form around these values, gives you:
y = (x - 1)² + 4.
Voila!