Chapter 5 Test (5-1 through 5-8)

Equation with Rational Roots

-Factor they perfect square trinomial -Square Root Property -Find the square root -Solve the equation using the positive and negative

Factored Form

0 = a(x - p) (x - q)

Graph a Quadratic Inequality

1.) Graph the Function 2.) Test a point 3.) If point is a solution shade area that includes the point/If point isn't a solution shade area that doesn't includes the point

Complex Numbers

Any number can be written in the form a + b*i*

Quadratic Inequalitites

Can graph in two variables by using the same techniques used to graph linear inequalities in two variables

Imaginary Unit (i)

Defined as *i*² = -1 *i* = √-1

Quadratic Function

In a quadratic function the greatest exponent is 2

Axis of Symmetry

Line through the graph of a parabola that divides the graph into two congruent halves

Zeros

One method for finding the roots of a quadratic equation is to find the zeroes of the quadratic function

Square Root Property

Putting the +/- in front of the radical

Quadratic Equation

Quadratic functions that are set equal to 0

Solve Quadratic Inequalities

Quadratic inequalities in one variable can be solved using the graphs of the related quadratic functions

Write an Equation Given Roots

Replace p and q with the roots [0 = a(x - p) (x - q)] Foil and simplify

Roots

Solutions of a quadratic equation

Pure Imaginary Numbers

Square roots of negative real numbers For any positive real number b, √-b² = √b² × √-1 or b*i*

Constant Term

Term in a quadratic function with no x term

Linear Term

Term in a quadratic function with the x term

Quadratic Term

Term in a quadratic function with the x² term

Vertex

The axis of symmetry will intersect a parabola at only one point

FOIL Method

Uses the Distributive property to multiply binomials

Maximum Value

Y-value of the vertex of a quadratic function (downwards opening)

Minimum Value

Y-value of the vertex of a quadratic function (upwards opening)

Standard Form

ax² + bx + c = 0 (a does not equal 0, a b and c are integers)

Discriminant

b² − 4ac (the part of the Quadratic formula under the square root) Can be used to determine the number and types of solutions

Vertex Form

y = a (x - h)² + k where (h, k) is the vertex x = h is the axis of symmetry a is the shape of the parabola