Key Terms - Elementary Algebra

Key Terms

axis of symmetry: The axis of symmetry is the vertical line passing through the middle of the parabola $y = a x^{2} + b x + c .$

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 $n$ , 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 $n$ , the next consecutive odd integer is $n + 2$ , and the next after that is $n + 4$ .

discriminant: In the Quadratic Formula, $x = \frac{− b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ the quantity $b^{2} - 4 a c$ 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 $a x^{2} + b x + c = 0$ , where $a \neq 0 .$

quadratic equation in two variables: A quadratic equation in two variables, where $a, b, and c$ are real numbers and $a \neq 0$ is an equation of the form $y = a x^{2} + b x + c .$

Square Root Property: The Square Root Property states that, if $x^{2} = k$ and $k \geq 0$ , 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 $x = 0 .$