In this lesson on Solving Equations by Graphing, our instructor guides you through the different types of solutions: two distinct solutions or roots, one double root, or no real roots. You will also learn how to estimate solutions when the graph does not intersect any of the axes on integer numbers.
equation is one that can be written in the form ax2 +
bx + c = 0, where a ≠ 0. Its solutions are called the roots
of the equation.
The roots of a
quadratic equation are x-intercepts of the graph of the related
equation has 2 real roots if its graph has two x-intercepts, 1 real
root if it has one x-intercept (in this case, the graph is tangent
to the x axis and the root is called a double root), and no
real roots if it has no x-intercepts.
If a root is not
an integer, estimate the root by stating the two consecutive
integers it lies between.
In general, use
graphing to solve an equation only if you would be satisfied with an
estimate for the solutions, not exact values.
A real number is a
zero of the quadratic function f(x) if and only if it is a root of
the equation f(x) = 0.
Solving Equations by Graphing
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.