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How do you factor an equation like ax^2+bx+c if the a is negative and there is no c?

I know how to graph these kinds of equations with parabolas but cannot figure out how to find the factored, vertex, and standard forms of these equations.

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2 Answers

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y = -x^2 + 4x

 

If so,

Standard form = -(x^2) + 4x

 

For vertex form,

Factor out the - sign to get the reflection/stretch (this is "a" in y=a(x-h)^2 + k

y = -(x^2 - 4x)

Complete the square:

y = -(x^2 - 4x + 4) + 4   (adding NEGATIVE 4 inside to complete the square. Do not forget the - factored outside the parentheses.  Since you added -4 to complete the square, you must add +4 outside to have a net effect of nothing being added or subtracted on that side of the equation.

 

y = -(x-2)^2 + 4

Vertex = (2,4)

 

Don't get confused by the fact that a is negative and c=0.  This is standard factoring.

ax^2+bx+c = (ax+b)(x)     Remember: c=0