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## PowerPoint Slideshow about ' S.4 Mathematics' - tammy

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(3, 4)

x + y –7 = 0

x

0

2x – 3y +6=0

Put (3,4) into x +y –7 =0

Put (3,4) into 2x –3y +6 =0

LHS = (2)3 – 3(4) + 6

LHS = 3+4 – 7

= 0

= 0

= RHS

= RHS

(3,4) is thesolutionof the equations of x +y –7 =0 and

2x –3y +6 =0

0

No points of intersection

x

What is the relationship between the number of pointsof intersection and the value of discriminant?

y

y

x

x

0

0

0

Case 1:2 points of intersection

∆ > 0

Case 2: 1 point of intersection

∆ = 0

Case 3:No point of intersection

∆ < 0

Determine the number of points of intersection of the parabola and the straight line.

Parabola:

Straight line:

There are two points of intersection

Determine the number of points of intersection of the parabola and the straight line.

Parabola:

Straight line:

There is no point of intersection

There are two points of intersection

There is one point of intersection

No point of intersection

Determine the number of points of intersection of the parabola and the straight line.

Parabola:

Straight line:

We can use :

I) Graphical method

II) Discriminant method

Any other method?

Determine the number of points of intersection of the parabola and the straight line.

Parabola:

Straight line:

We can use :

I) Graphical method

II) Discriminant method

Any other method?

∴(3,4) and (-2,-8) are the 2 points of intersection.

Which method is the fastest in determining the number of points of intersection of the parabola and the straight line?

I) Graphical method

II) Discriminant method

III) Solving the simultaneous equations

(Algebraic method)

1. If the parabola y = – x2 + 2x + 5 and the line y = k intersect at one point, find the value of k.

If the parabola and the line intersect at one point , then the discriminant equals to zero.

24 – 4k = 0

∴ k = 6

2. If the straight line y = 3x + kdoes not cut the parabola y = x2 – 3 x + 2 at any point, find the range of values of k.

There is no point of intersection

3. If the straight line 2x – y – 1 = 0 cuts the parabola y = 3 x2 + 5x + k at two points, where k is an integer. Find the largest value of k.

There are two points of intersection so the discriminant is greater thanzero.

∴ k < – 0.25

– 3 – 12 k > 0

The largest value of k is – 1

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