In a parabola defined by the equation ( y = ax^2 + q ), the parameter ( a ) determines the direction and width of the parabola, while ( q ) represents the vertical shift. To solve the effect of ( a ), consider its value: if ( a > 0 ), the parabola opens upward and is narrower as ( |a| ) increases; if ( a < 0 ), it opens downward and becomes wider as ( |a| ) decreases. The parameter ( q ) shifts the entire parabola up or down by ( q ) units without altering its shape. Adjusting these parameters allows for a comprehensive understanding of the parabola's position and orientation in the coordinate plane.
what are the effects of the sign a and n to the parabola
If the equation of the parabola isy = ax^2 + bx + c then the roots are [-b +/- sqrt(b^2-4ac)]/(2a)
No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.
q = 78
Once you calculate the X coordinate using the axis of symmetry (X=-b/2a), you plug that value in for all of the X's in the equation of the parabola. You then solve the equation for the value of Y.
what are the effects of the sign a and n to the parabola
Today we'll study the parabola effect.
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
If the equation of the parabola isy = ax^2 + bx + c then the roots are [-b +/- sqrt(b^2-4ac)]/(2a)
Set y = 0 and solve for x, with a parabola you should get one, two, or no x-axis crossings, it depends on the equation and the location on the x-y axis of the parabola.
No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.
If you know the equation, you just plug in x = 0 and solve.
q = 78
By factoring. q2 + 16q = 0 q (q + 16) = 0 Now, either q = 0, or q + 16 = 0. Solve those two equations to get the solution.
3q = 18 q = 6
The focus of a parabola is a fixed point that lies on the axis of the parabola "p" units from the vertex. It can be found by the parabola equations in standard form: (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h) depending on the shape of the parabola. The vertex is defined by (h,k). Solve for p and count that many units from the vertex in the direction away from the directrix. (your focus should be inside the curve of your parabola)
q=4k+4uImproved Answer:-If: Q = 4k+4uThen: k = (4u-Q)/-4