# Tag Archives: parabola

## Three Consecutive Odd Numbers

Find three consecutive odd numbers such that the sum of their squares is a four-digit number with all four digits the same. Source: NCTM Mathematics Teacher, February 2008 Solution The squares of odd numbers are odd and the sum of … Continue reading

## Product of Consecutive Integers

How many integer pairs satisfy the equation ? Source: NCTM Mathematics Teacher, September 2006 Solution We construct products of positive consecutive integers and see which ones if any can be expressed as a power of . is the only such … Continue reading

## Spring Garden

Each spring, a meter by meter garden has its length increased by meters but its with decreased by centimeters. What will be the maximum attainable area of the garden? Source: NCTM Mathematics Teacher, October 2006 Solution Area in square meters … Continue reading

## 2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

## Equation of Parabola

A parabola with integral roots passes through the points and . Find the equation of this parabola. Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let be the equation of the parabola. At point At point Rewrite Eq. Substitute the value … Continue reading

## Largest Value

The equilateral triangle has side length , and is a point on the line segment . Denote by the area of triangle and by the area of triangle . What is the largest value of the product ? Source: NCTM … Continue reading

## Parabola Passing Through Three Points

Three points , and form the vertices of an equilateral triangle. Find the equation of the parabola that passes through these three points. Source: NCTM Mathematics Teacher SOLUTION is the vertex and the focus of the parabola. Let be the … Continue reading