How Do You Graph a Quadratic Equation with No Solution?

Note:

One of the many ways you can solve a quadratic equation is by graphing it and seeing where it crosses the x-axis. Follow along as this tutorial shows you how to graph a quadratic equation to find the solution. Check it out!

Keywords:

problem
skill
quadratic equation
graphing
0 solutions
no solution
solve
zeros

Background Tutorials

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the Y-Coordinate?
  
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the y-coordinate in an ordered pair!
- What is the X-Axis?
  
  To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the x-axis and see where it's located in the coordinate plane.
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
- How Do You Plot Points in the Coordinate Plane?
  
  Knowing how to plot ordered pairs is an essential part of graphing functions. In this tutorial, you'll see how to take an ordered pair and plot it on the coordinate plane. Take a look!
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- What is a Polynomial?
  
  If you learn about algebra, then you'll see polynomials everywhere! In this tutorial, you'll learn the definition of a polynomial and see some of the common names for certain polynomials.
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- How Do You Make a Table for a Quadratic Function?
  
  When you're trying to graph a quadratic equation, making a table of values can be really helpful. To figure out what x-values to use in the table, first find the vertex of the quadratic equation. That way, you can pick values on either side to see what the graph does on either side of the vertex. To see how to make a table of values for a quadratic equation, check out this tutorial!
- What is the Axis of Symmetry of a Quadratic Function?
  
  Ever notice that the left side of the graph of a quadratic equation looks a lot like the right side of the graph? In fact, these sides are just mirror images of each other! If you were to cut a quadratic equation graph vertically in half at the vertex, you would get these symmetrical sides. That vertical line that you cut has a special name. It's called the axis of symmetry. To learn about the axis of symmetry, watch this tutorial!
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.
- What is a Quadratic Equation?
  
  You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!
Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- How Do You Find the a, b, and c Values of a Quadratic Function?
  
  When you're dealing with quadratic equations, it can be really helpful to identify a, b, and c. These values are used to find the axis of symmetry, the discriminant, and even the roots using the quadratic formula. It's no question that it's important to know how to identify these values in a quadratic equation. This tutorial shows you how!
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- What is the Vertex of a Quadratic Function?
  
  Each quadratic equation has either a maximum or minimum, but did you that this point has a special name? In a quadratic equation, this point is called the vertex! Take a look at the vertex of a quadratic equation by watching this tutorial.
- What is a Quadratic Function?
  
  You can't go through algebra without seeing quadratic functions. The graphs of quadratic functions are parabolas; they tend to look like a smile or a frown. In this tutorial, get introduced to quadratic functions, look at their graphs, and see some examples of quadratic functions!