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GCSE Mathematics Problem Solving Algebra Higher Tier

GCSE Mathematics Problem Solving Algebra Higher Tier. The curve y = x 2 +2x - 15 intersects the x axis at points A and B. Find the length of the line AB?. To find the length of AB you need to know the coordinates of A and B . Next consider how to find the coordinates of the points A and B .

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GCSE Mathematics Problem Solving Algebra Higher Tier

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  1. GCSE Mathematics Problem Solving Algebra Higher Tier

  2. The curve y = x2 +2x - 15intersects the x axis at points A and B. Find the length of the line AB? • To find the length of AB you need to know the coordinates of A and B • Next consider how to find the coordinates of the points A and B • When the curve intersects the x-axis y = 0. • Therefore, • 0 = x2 +2x - 15 • Solve the quadratic equation to find the values for x that satisfy the equation.

  3. 0 = x2 +2x - 15 • The first step in solving this equation is to factorise. • What two terms multiply to make x2 ? • ( )( ) • x • + 5 • x • - 3 • What two numbers multiply to make -15 and add to give + 2? • x – 15 • 1 x – 15 • -1 x 15 • 3 x -5 • -3 x 5 • Add + 2 • -14 • 14 • -2 • 2

  4. 0 = (x + 5)(x – 3) • So, • x + 5 = 0 or x – 3 = 0 • If • x + 5 = 0 then x = -5 • These values are the x coordinates for A and B. The y coordinates will be ‘0’ for both A and B • If • x - 3 = 0 then x = 3 • A ( -5, 0) B(3, 0) • Sketch the curve y = x2 +2x – 15 to help find the length of the line AB

  5. Both points lie on the x axis, so we can see from the sketch that the distance between the points (-5,0) and (3,0) is the difference between the x coordinates. So AB is equal to 8 units.

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