sunshine022uv

2021-12-22

Explain how to find the vertex of a parabola in standard form.

recoronarrv

The standard form of a parabola: $y=a{x}^{2}+bx+c$, where $a\ne 0$
The vertex is the minimum or maximum point of a parabola. If $a>0$, the vertex is the minimum point and the parabola opens upward. If $a<0$, the vertex is the maximum point and the parabola opens downward.
If you want to find a vertex, you need to find the x- and y-coordinates.
The formula for the axis of symmetry and the x-coordinate of the vertex: $x=\frac{-b}{2a}$
To find the y-coordinate of the vertex, substitute the value for x into the equation and solve it for y.
$y=a{\left(\frac{-b}{2a}\right)}^{2}+b\left(\frac{-b}{2a}\right)+c$

Melissa Moore

When the axis and the perpendicular tangent at the vertex $V\left(\alpha ,\beta \right)$ are parallel to the coordinate axes, the standard form is:
${\left(y-\beta \right)}^{2}=±4a\left(x-\alpha \right)$ or ${\left(y-\alpha \right)}^{2}=±4a\left(x-\beta \right)$

user_27qwe