Quadratics Vocabulary

Karis Thomas

Parabola

A special curve, shaped like an arch.


When graphing the distance a ball is in the air after being kicked, the line creates a parabola.

Quadratic

Involving the second and no higher power of an unknown quantity or variable


The equation 5x^2-3x+3 = 0 is a quadratic equation because the highest power ^2, causes it to be quadratic. Even if the equation looked like: y = 5x^2 - 3x, its still quadratic because it has the "A^2" or 5x^2, in the equation.

Vertex

The "point" of a parabola is the vertex; the 'tip' of the curve.


An example of a vertex would be like the picture to the right. The vertex is written as (x,y). To find y (in order to plug in values for x and y) you take the x value and plug it into the original quadratic equation.

Axis of Symmetry

A line through a shape so that each side is a mirror image


The axis of symmetry on a parabola shows that both sides of the axis is symmetrical. To find the axis of symmetry or the x value, you use the formula -b/2a. Remember that the value with the ^2 is a and the middle value with x is b.

Maximum & MInimum Value

The largest value


The maximum of a parabola is only there when the parabola is faced down. When faced up, the parabola's value would be minimum.

Terms

A term is either a number or a variable, or numbers and variables multiplied together.


Terms are either added or subtracted from each other to find a factored, simplified or finalized product. There can be more than one term in an expression/equation. Examples of terms are: x^2 + 2x + 3. There are 3 terms here because x^2 is one term, 2x is the second term and 3 is the last term!

First Difference

A first difference is the difference you get when subtracting the x values from each other and y values from each other to find a constant value. The x values ad y values will have a common difference.


An example of first difference would be:

X values: 0, 1, 2, 3, 4

Y values: 5, 7, 9, 11, 13


*Remember to subtract the sec. from the first!! When you subtract 0 from 1, you get 1. When you subtract 1 from 2, you get 1. When you subtract 2 from 3, you get 1. So on and so forth... Now do the same thing for the Y values. See a common difference? It's 2!

Second Difference

To find the second difference, you take the first difference numbers (IF THEY ARE NOT CONSTANT) from the y values and subtract them as if you're finding a constant for those numbers. You will notice that the second differences do have a constant difference!


An example of second difference would be:

X values: 0, 1, 2, 4, 5...

Y values: 1, 2, 4, 7, 11, 16, 22...

Y val. first difference: 1, 2, 3, 4, 5, 6

Y va. second difference: 1, 1, 1, 1, 1, 1


*Remember to subtract the sec. from the first!! Notice how the first differences weren't the same. When you subtract those numbers, you get a constant difference.

Zeros (Roots)

Zeros or roots are basically the x-intercepts of a parabola, where the parabola crosses the x axis. A parabola can have one, two, or no zeros.


If a parabola crossed the x axis twice on 4 and -4, the zeros of that parabola is 4 and -4.