Key Terms Chapter 10: Quadratic Equations
- Page ID
- 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 \(𝑥=0\).