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An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)

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Yes, a parabola always has a vertex. However, it may not always have roots. The roots of a parabola are the x-values where the parabola intersects the x-axis. It is possible for a parabola to have two, one, or no roots depending on the discriminant of the quadratic equation.

Q: Does a parabola always have roots and a vertex?

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In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.

Suppose the equation of the parabola is y = ax2 + bx + c where a, b, and c are constants, and a â‰ 0. The roots of the parabola are given by x = [-b Â± sqrt(D)]/2a where D is the discriminant. Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a. It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.

The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!

The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.

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There's the vertex (turning point), axis of symmetry, the roots, the maximum or minimum, and of course the parabola which is the curve.

In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.

The vertex would be the point where both sides of the parabola meet.

Suppose the equation of the parabola is y = ax2 + bx + c where a, b, and c are constants, and a â‰ 0. The roots of the parabola are given by x = [-b Â± sqrt(D)]/2a where D is the discriminant. Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a. It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.

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.

To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.

The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!

The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.

The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.

the vertex of a parabola is the 2 x-intercepts times-ed and then divided by two (if there is only 1 x-intercept then that is the vertex)

The vertex -- the closest point on the parabola to the directrix.

i think that the range and the domain of a parabola is the coordinates of the vertex