WAEC SSCE - General Mathematics - 2018 (Objective)

Question 1 Report

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 = $x^2 - x - 6$

Answer Details

We are given that the curve passes through the points $(-2, 0)$ and $(3, 0)$. Since the curve is a function of $x$, we can assume that the equation of the curve is of the form $y = f(x)$. If the curve passes through the point $(-2, 0)$, then we can substitute $x = -2$ and $y = 0$ into the equation of the curve to get: $$ 0 = f(-2) $$ Similarly, if the curve passes through the point $(3, 0)$, then we can substitute $x = 3$ and $y = 0$ into the equation of the curve to get: $$ 0 = f(3) $$ Therefore, the curve must have at least two roots, namely $x = -2$ and $x = 3$. This suggests that the curve is a quadratic function. We can use the information about the roots of the curve to write the equation of the curve in factored form: $$ y = A(x + 2)(x - 3) $$ where $A$ is a constant. Since the coefficient of $x^2$ in the equation is 1, we can simplify this equation to: $$ y = Ax^2 + Bx + C $$ where $A = 1$, and $B$ and $C$ are constants. To find the values of $B$ and $C$, we can substitute the points $(-2, 0)$ and $(3, 0)$ into the equation: $$ 0 = A(-2)^2 + B(-2) + C \quad \text{and} \quad 0 = A(3)^2 + B(3) + C $$ Simplifying these equations, we get: $$ 4A - 2B + C = 0 \quad \text{and} \quad 9A + 3B + C = 0 $$ We can use these two equations to solve for $B$ and $C$. Adding the two equations, we get: $$ 13A + B = 0 $$ Substituting this expression for $B$ into one of the previous equations, we get: $$ 4A - 2(-13A) + C = 0 $$ Simplifying, we get: $$ 20A + C = 0 $$ Solving these two equations simultaneously, we get: $$ A = \frac{1}{13}, \quad B = -\frac{4}{13}, \quad C = 0 $$ Therefore, the equation of the curve is: $$ y = \frac{1}{13}(x + 2)(x - 3) = \frac{1}{13}(x^2 - x - 6) $$ So the correct answer is $y = x^2 - x - 6$.

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Application Of Differentiation (JAMB)






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