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• Created by: Ice_Fox
• Created on: 29-09-21 11:28

## Sketch a quadratic (3 marks)

1 mark - shape of the curve

1 mark - coordinates of the x and y intercepts

1 mark - coordinates of the min/max

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## The shape of the curve

- parabola

- u shape if the coefficient on xis positive

- n shape if the coefficient on x2  is negative

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## Coordinates of the x and y intercepts

Y-intercept

- substitute x=0 into the equation

- e.g. y = ax2 + bx + c

y = 0x2 + 0x + c

y = c

X-intercepts

- substitute y=0 into the equation

- e.g. y = x2 + 5x + 6

0 = x2 + 5x + 6

0 = (x + 3) (x + 2)

x = -3  OR  x = -2

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## Number of real roots

Put it in the form: ax2 + bx + c =0

The disciminant: b- 4ac

If...

b2 - 4ac > 0  it has 2 distinct real roots / crosses the x-axis twice

b2 - 4ac = 0  it has 1 real root (or two repeated roots) / crosses the x-axis once

b2 - 4ac < 0  it has no real roots / never crosses the x-axis

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## Coordinates of min/max

Positive coefficient on x2 = Minimum

Negative coefficient on x2 = Maximum

To find min/max:

- complete the square

- e.g. (x - p)2 + q

- Min/Max = (p, q)

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## Line of Symmetry

Complete the square: (x - p)2 + q

The line of symmetry: x = p

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