factorising and quadratic graphs l.
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FACTORISING AND QUADRATIC GRAPHS. The solutions to any quadratic equation are easily related to their underlying graphs. y. i) Solve the equation x 2 ‒ 2 x ‒ 8 = 0. ( x + 2)( x ‒ 4) = 0. x = ‒2 or x = 4 . x. ii) The graph of y = x 2 ‒ 2 x ‒ 8.

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Presentation Transcript
slide2

The solutions to any quadratic equation are easily related to their underlying graphs.

y

i) Solve the equation

x2 ‒ 2x ‒ 8 = 0

(x + 2)(x ‒ 4) = 0

x = ‒2 or x = 4

x

ii) The graph of y = x2 ‒ 2x ‒ 8

7 0 5 8 98 5 0 7

slide3

And again……

y

i) Solve the equation

x2 + 2x ‒ 3 = 0

(x + 3)(x ‒ 1) = 0

x = ‒3 or x = 1

ii) The graph of y = x2 + 2x ‒ 3

0 34 3 0 5 12

x

slide4

Now to apply our work to sketch graphs……

y

i) Solve the equation

2x2 ‒ x ‒ 6 = 0

(2x + 3)(x ‒ 2) = 0

x = ‒1.5 or x = 2

ii) The graph of y = 2x2 ‒ x ‒ 6

x

2

1.5

2

0

1.5

0

0

6

6

slide5

And again……

y

i) Solve the equation

2x2 + 3x ‒ 5 = 0

(2x + 5)(x ‒ 1) = 0

x = ‒2.5 or x = 1

ii) The graph of y = 2x2 + 3x ‒ 5

1

x

2.5

1

0

2.5

0

0

5

5