Question

In a standard form:
Vertex:
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Answer 1

The question refers to finding the vertex in the context of the standard form of a quadratic equation. The vertex can be found by converting the standard form to the vertex form via completing the square. The vertex represents the highest or lowest point on the graph of a parabola.

Step-by-step explanation:

The question seems to be asking about the vertex in the context of a standard form of an equation, which is typically related to the vertex form of a quadratic equation. In mathematics, particularly in algebra, the standard form of a quadratic equation is usually given as ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. However, when referring to the vertex, one might be speaking of the vertex form of the equation, which is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola represented by the quadratic equation.

To convert the standard form to vertex form, one completes the square on the x-terms. Here is a simple step-by-step process on how that might be done:

1. Begin with the standard form: ax2 + bx + c.
2. Divide the entire equation by a to make the coefficient of x2 equal to 1 if it isn't already.
3. Rearrange the equation as (x2 + (b/a)x) + c.
4. Add and subtract (b/2a)2 within the parenthesis to complete the square.
5. Rewrite the completed square part as (x + b/2a)2 and simplify the constant terms.
6. The equation is now in the form y = (x + b/2a)2 + k, and thus the vertex is (-b/2a, k).

The vertex of a parabola in a quadratic equation is a crucial point as it represents the highest or lowest point on the graph, depending on the direction in which the parabola opens.