What is a Quadratic Equation?
How many solutions are there always found in a Quadratic Equation?
2
Graphing a Quadratic Equation looks like this
Do you see how it looks like our swing swinging back and forth? All quadratics will graph into some kind of similar curve. Some will be shifted higher, some will be shifted lower, some will be thinner, some wider, and some may even be sideways. But one thing is for sure, they will always graph into a curve.
Look at the parabola that is below the x-axis in Card #6. Now, look at the x-axis. Do you see that the graph now crosses the x-axis at two different spots? These give us our two real solutions.
Figure 1 in the graph in card #6
What is a Real Quadratic Solution and an Imaginary Quadratic Equation?
If we have two real solutions, then we have no imaginary solutions. If we have one real solution, then the other is an imaginary solution. If we have no real solutions, then we have two imaginary solutions. The number of real solutions depends on how many times the graph crosses the x-axis. If it doesn't cross, then all the solutions are imaginary.
Which of the following is NOT an example of a quadratic equation in real life?
a. The Yellow Arcs on a McDonalds sign b. Electric Wires hanging down from 2 poles. c. The Tennis ball in a Tennis Game d. The Path of a Speed Boat.
Notice that all of these functions are of degree 2, meaning that their highest exponent is a 2.
y = x² + 3x + 1 y = x² y = 2x² + 4x - 9 y = x² - 9 A = π * r²
What shape is a Quadratic Function or Equation?
It is the shape of a parabola
What is a Quadratic Equation?
Picture a swing swinging back and forth. If you were watching it from side to side, what kind of shape does it seem to outline? Why, isn't it an arc of some sort? Or, does it look like the shape of a partial circle? Yes and yes! This shape that the swing outlines is an example of what a quadratic equation gives you when you graph it. In Algebra, we define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2.
What is a Real Solution?
Solutions are where the quadratic equals 0. Real solutions mean that these solutions are not imaginary and are real numbers.
What is the Equation of a Standard Quadratic Equation?
The standard form of a quadratic equation is y = ax + bx² + c, where a, b, and c are numbers and a cannot be 0.
