Question

How do find the vertex of a parabola in standard form?

Answer 1

In the given question, we have been asked how to write the vertex of a parabola in standard form. We know that the vertex of parabola is the minimum or maximum point depending on the sign of the vertex. The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.

Complete Step by Step Solution:
The standard form of a parabola is $a{x^2} + bx + c = 0$.
Now, the vertex is minimum when $a > 0$ and it is maximum $a < 0$.
To find the vertex, we need to find the abscissa and ordinate.
The formula for x-coordinate of the vertex is:
$x = - \dfrac{b}{{2a}}$
To find the y-coordinate, we substitute the value of $x$ in the standard parabolic equation,
$y = a{\left( { - \dfrac{b}{{2a}}} \right)^2} + b\left( { - \dfrac{b}{{2a}}} \right) + c$
Hence, the standard form of the vertex is $V\left( { - \dfrac{b}{{2a}},a{{\left( { - \dfrac{b}{{2a}}} \right)}^2} + b\left( { - \dfrac{b}{{2a}}} \right) + c} \right)$.

Note:
In the given question, we had to find the standard form of the vertex of a parabola. For finding any part of a figure in the standard form, we first always convert the given equation into the standard form of the equation. Then we use the available options in the standard form so as to get to the standard form of the required part.