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#### Resources tagged with Quadratic functions similar to Integral Inequality:

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### Integral Inequality

##### Stage: 5 Challenge Level:

An inequality involving integrals of squares of functions.

### Converse

##### Stage: 4 Challenge Level:

Clearly if a, b and c are the lengths of the sides of a triangle and the triangle is equilateral then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true, and if so can you prove it? That is if. . . .

### Geometric Parabola

##### Stage: 4 Challenge Level:

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

### ' Tis Whole

##### Stage: 4 and 5 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?

##### Stage: 5 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?

### Parabella

##### Stage: 5 Challenge Level:

This is a beautiful result involving a parabola and parallels.

##### Stage: 4 Challenge Level:

Explore the relationship between quadratic functions and their graphs.

### Consecutive Squares

##### Stage: 4 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?

### More Parabolic Patterns

##### Stage: 4 and 5 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.

### Parabolas Again

##### Stage: 4 and 5 Challenge Level:

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

### Alison's Mapping

##### Stage: 4 Challenge Level:

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

### Parabolic Patterns

##### Stage: 4 and 5 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.

##### Stage: 4 Challenge Level:

Here are some more quadratic functions to explore. How are their graphs related?

##### Stage: 4 Challenge Level:

Explore the two quadratic functions and find out how their graphs are related.

### Spaces for Exploration

##### Stage: 3 and 4

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

### Grid Points on Hyperbolas

##### Stage: 5 Challenge Level:

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

### Minus One Two Three

##### Stage: 4 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 ?