markwjak said:Homework Statement
write the standard form of the equation
x^2-4x+8y+12=0
find the focus
Homework Equations
The Attempt at a Solution
i have it down to (x-2)^2=-8(y-8)
i'm not sure if you have to multiply the -8 on the right side of the equations by 4 since the focus is 1/4a
The general form of a parabola is y = ax^2 + bx + c, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term.
The standard form of a parabola is y = a(x-h)^2 + k, where a is the coefficient of the squared term, and (h,k) is the vertex of the parabola.
To convert a parabola from general form to standard form, you can use the process of completing the square. This involves manipulating the general form equation to get it in the form of y = a(x-h)^2 + k, where h and k can be determined from the original equation.
The coefficient a represents the direction and shape of the parabola, with positive values creating a "U" shape and negative values creating an upside down "U" shape. The coefficient b controls the horizontal position of the parabola, and c determines the vertical position.
To graph a parabola given in standard form, first plot the vertex at the point (h,k). Then, use the value of a to determine the direction and shape of the parabola. If a is positive, the parabola will open upwards, and if a is negative, it will open downwards. Finally, use the x-intercepts, which can be found by setting y equal to 0 and solving for x, to plot additional points and complete the graph.