Arc De Triomphe
Quadratics
Quadratics and Their Function
1. What's a Quadratic Equation?
As explained in the polynomial section, a "quadratic" equation is an equation where the highest exponential value is 2.
2. What are Quadratic Equations used for?
Quadratic equations have mainly just one purpose. They are the symbolic representation of the graph of a parabola. When numbers are inputted into them, the points that result are the points on the graph.
What do they look like?
Quadratic equations all have a highest exponent of two. The most simplest quadratic is f(x)=x^2. If you recall from the polynomials section, this is a quadratic because it has a highest exponent of two. Other quadratic equations can look like f(x)=2x^2+7x-3, or f(x)=9x^2+2.
How do you graph parabolas with them?
To graph quadratic equations, such as a parabola, you need to know the vertex and a few other points. You plug in a number for x, and solve. Whatever the answer is is the y-ccordinate of the point. You could also find the zeroes of the graph. The zeroes is the x - intercept, or where the graph hits the x-axis. One way to do this is to factor out the equation to (x+m)(x+n), where m and n are the facotred numbers. To factor out, you add the a and c values, then the factors of the resulting number must add up to b. The zeroes would be the inverses of m and n. Another way to do this is set the equation equal to 0, then solve. The other zero will usually be the inverse of that. To find the vertex, just look at the equation. If it's in the format f(x)=a(x-h)^2+c, then the inverse of "h" is the vertex's x-coordinate, and the "c" value is the y-coordinate of the vertex.