Resources tagged with: Quadratic functions and graphs

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There are 14 results

Broad Topics > Coordinates, Functions and Graphs > Quadratic functions and graphs

Parabolic Patterns

Age 14 to 18 Challenge Level:

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

More Parabolic Patterns

Age 14 to 18 Challenge Level:

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Janusz Asked

Age 16 to 18 Challenge Level:

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

Parabolas Again

Age 14 to 18 Challenge Level:

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

Grid Points on Hyperbolas

Age 16 to 18 Challenge Level:

Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.

Parabella

Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

Which Quadratic?

Age 14 to 18 Challenge Level:

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

' Tis Whole

Age 14 to 18 Challenge Level:

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

Guessing the Graph

Age 14 to 16 Challenge Level:

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Minus One Two Three

Age 14 to 16 Challenge Level:

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

Consecutive Squares

Age 14 to 16 Challenge Level:

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Integral Inequality

Age 16 to 18 Challenge Level:

An inequality involving integrals of squares of functions.

Converse

Age 14 to 16 Challenge Level:

Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?

Geometric Parabola

Age 14 to 16 Challenge Level:

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.