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.
How do you factor an equation like ax^2+bx+c if the a is negative and there is no c?
y = -x^2 + 4x
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