# Interesting quadratic patterns

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## Lesson details

### Key learning points

- In this lesson, we will explore different patterns related to quadratics and square numbers.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 6 Questions

Q1.

Select the words that best fill in the gaps in order: The __________ is where the curve crosses the y axis, when _______.

x intercept, x=0

x intercept, y=0

y intercept, y=0

Q2.

What are the coordinates of where y= x² + 14x + 24 crosses the y axis?

(0, 10)

(0, 14)

(24, 0)

24

Q3.

Where does y = x² - 3x - 10 cross the y axis?

(-3, -10)

(10, 3)

(3, 10)

Q4.

Which graph could be a sketch of y=(x+4)(x-3)?

Option A

Option B

Option C

Q5.

Which graph could be a sketch of -x² + 3x - 2? Hint Try out some coordinates to check!

Option A

Option B

Option D

Q6.

Zaki says y = x² + 1 will never cross either axes. Is that correct?

Zaki is correct, the curve will never cross either axes.

Zaki is incorrect the curve wil cross the x axis only.

Zaki is incorrect the curve will cross BOTH axes.

### 6 Questions

Q1.

Which of the following could represent 3 consecutive integers?

n, 2n, 3n

n, n+3, n+6

None of the above,

Q2.

I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Which example could be my calculation?

(4 x 3)- 3²

(4 x 3)- 4²

3² - (4 x 3)

Q3.

I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Write out some examples of these. What do you notice about the answers?

The answer is always a cube number.

The answer is always bigger than both of the original numbers.

The answer is always the square of one of the original numbers.

Q4.

I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Which example could be an algebraic representation of this situation?

4(n+1)- n²

4n- (n+1)²

n² - 4(n+1)

Q5.

I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Zaki writes a different algebraic expression to me but is still correct. Which one could he have written?

(n-1)² - 4(n+1)

(n-1)² - 4n

4n- (n-1)²

Q6.

I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Alex and Steven have both tried to generalise my pattern. Who is correct?

Alex and Steven are both incorrect.

Just Alex is correct.

Just Steven is correct