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What is a Parabola?

Q: What are parabolas?

A: Parabolas are conic sections. The standard form is

The vertex is located at (p,q)

♦  Note that (x-p) means that the x-coordinate of the vertex is p ♦  Conversely, (x+p) means that the x-coordinate of the vertex is at -p

a is the ‘slope’ of the parabola, determining . . . → Read More: What is a Parabola?

Graphing a Parabola

Q: What if I don’t have an Equation Solver, how do I graph a parabola?

A: The easiest way is to make a table of values. To keep things simple, let’s look again at . To generate a table of values, simply substitute different values of x to obtain the corresponding value of y. . . . → Read More: Graphing a Parabola

Changing the value of a in Parabola equation y=a(x-p)^2+q

Q: What happens if I change the value of a?

A: This affects the steepness or ‘slope’ of the parabola.

Let’s compare 3 graphs with different a values: a=2, a=1, and a=0.5

Max/Min Problem, Difference of Two numbers

Q: Two numbers hava a difference of 16. Find the numbers if their product is a minimum.

A: Let x = first number Let y = second number

Equation 1: x-y = 16 Equation 2: xy=P , where P is the product.

You need to isolate for x or y in Equation 1, and . . . → Read More: Max/Min Problem, Difference of Two numbers

Inverse of a Parabola

Find the inverse of

Step 1: Re-write the function so that y replaces f(x):

Step 2: Swap the values of y and x. This means, anywhere there is an x, make it y, and anywhere there is a y, make it x.

Step 3: Re-arrange the formula so that y is . . . → Read More: Inverse of a Parabola