Key Terms

Key Terms

axis of symmetry

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

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 $n$, 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, $x=\frac{\text{−}b\pm \sqrt{b^2-4ac}}{2a}$ 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 $a{x}^2+bx+c=0$, where $a\ne 0.$

quadratic equation in two variables

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

Square Root Property

The Square Root Property states that, if $x^2=k$ and $k\ge 0$, then $x=\sqrt{k}\text{or}x=\text{−}\sqrt{k.}$

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 $x=0.$