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Key Terms Chapter 10: Quadratic Equations

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    101931
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    Axis of Symmetry
    The axis of symmetry is the vertical line passing through the middle of the parabola \(y=ax^2+bx+c\).
    Completing the Square
    Completing the square is a method used to solve quadratic equations.
    Consecutive Even Integers
    Consecutive even integers are even integers that follow right after one another. If an even integer is represented by 𝑛n, the next consecutive even integer is \(n+2\), and the next after that is \(n+4\).
    Consecutive Odd Integers
    Consecutive odd integers are odd integers that follow right after one another. If an odd integer is represented by 𝑛n, the next consecutive odd integer is \(n+2\), and the next after that is \(n+4\).
    Discriminant
    In the Quadratic Formula, \(x=\frac{-b±\sqrt{b^2-4ac}}{2a}\) the quantity \(b^2−4ac\) is called the discriminant.
    Parabola
    The graph of a quadratic equation in two variables is a parabola.
    Quadratic Equation
    A quadratic equation is an equation of the form \(ax^2+bx+c=0\), where \(a≠0\).
    Quadratic Wquation in Two Variables
    A quadratic equation in two variables, where \(a\), \(b\), and \(c\) are real numbers and \(a≠0\) is an equation of the form \(y=ax^2+bx+c\).
    Square Root Property
    The Square Root Property states that, if \(x^2=k\) and \(k≥0\), then \(x=\sqrt{k}\) or \(x=−\sqrt{k}\).
    Vertex
    The point on the parabola that is on the axis of symmetry is called the vertex of the parabola; it is the lowest or highest point on the parabola, depending on whether the parabola opens upwards or downwards.
    \(x\)-intercepts of a Parabola
    The \(x\)-intercepts are the points on the parabola where \(y=0\).
    \(y\)-intercept of a Parabola
    The \(y\)-intercept is the point on the parabola where \(𝑥=0\).
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