A conic is a curve formed by the intersection of a plane and a cone. It can be classified as a circle, ellipse, parabola, or hyperbola.
The standard form of a parabola is y = ax^2 + bx + c, where a, b, and c are constants and a cannot be equal to 0.
To rewrite a parabola into standard form, you can use the process of completing the square or the quadratic formula. First, make sure the equation is in the form y = ax^2 + bx + c. Then, complete the square by adding (b/2)^2 to both sides of the equation. Finally, factor the trinomial and simplify to get the equation in standard form.
The vertex form of a parabola is y = a(x - h)^2 + k, where a is the same as in standard form, and (h, k) represents the coordinates of the vertex. This form is useful for quickly identifying the vertex and direction of opening of the parabola.
Yes, a parabola can open downwards if the coefficient a is negative in the standard form equation. This means that the vertex will be the highest point on the parabola, and the graph will be a reflection of a parabola that opens upwards.