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WAEC Mathematics 2018 Paper

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Question : 12

Total: 50

A curve is such that when y = 0, x = -2 or x = 3. Find the equation of the curve.

y = $x^2 - 5x - 6$
y = $x^2 + 5x - 6$
y = $x^2 + x - 6$
y = $x^2 - x - 6$

Solution:

Concept:

If a curve cuts the x-axis at

x = -2

and

x = 3

, then

x = -2

and

x = 3

are the roots of its equation.

Explanation:

When

y = 0

, the given values are

x = -2

and

x = 3

.

So the factors of the equation are

(x + 2)

and

(x - 3)

.

Therefore,

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

.

Expand:

x^2 - 3x + 2x - 6 = 0

.

Simplify:

x^2 - x - 6 = 0

.

Hence, the required equation of the curve is

y = x^2 - x - 6

.

Answer:

Option D:

y = x^2 - x - 6

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