Concepts of Intercepts, Zeros, and Solutions

Intercepts, Zeros, and Solutions:

Chapter Summary:

The Zeros or roots of functions and solutions to the equations can either be complex or real numbers. X-intercepts can only be real numbers.

TI graphing calculator can be utilized to determine the real roots of the equation.

All calculators:

a) When your equation has anything on the right side, subtract it from both sides and hence the right hand side is equal to 0.

b) Go to Y=

c) Now, enter the expression.

d) Hit the Graph.

e) Modify the viewing window when essential and hence we can see where the graph crosses the x-axis. We require making sure that there is sufficient to left and right of the x-intercept to choose a point.

f) Carry on to the particular steps for your calculator. When there is more than one x-intercept, you might require changing your viewing window and repeat the steps for all x-intercept.

Basic definitions:

Equation: It is a statement in which two algebraic expressions are equivalent.

Solutions: All values of variable for which the equation is accurate.

Linear equation in one variable x: The equation which can be written in the standard form of ax + b = 0 where a and b are the real numbers with a ≠ 0.

Mathematical modeling: It is the procedure of converting verbal descriptions to the algebraic equations in order to resolve a real-life problem.

Key topics included:

A) Linear Equations and Modeling
B) Solving Equations Graphically
C) Complex Numbers
D) Solving Equations Algebraically
E) Solving Inequalities Algebraically and Graphically
F) Exploring Data: Linear Models and Scatter Plots

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