What quadratic characteristics can we find on a graph?

• The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex.

• If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.

• If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

• The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry.

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What quadratic characteristics can we find on a equation?

• The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex.

• If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.

• If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

• The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry.

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What are the roots of a quadratic?

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.

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How do we complete the square?

Completing the square is a method that is used for converting a quadratic expression of the form ax2 + bx + c to the vertex form a(x - h)2 + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)2 + n, such that the left side is a perfect square trinomial.

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What is the quadratic formula?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The important condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term (a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written.

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