Find the minimum value of y = 3x² - x - 6.

Correct Answer is : −6 112-6\;1/12−6121

Correct Answer is : −6 112-6\;1/12−6121

Test Index

WAEC Further Mathematics 2016 Paper

Question : 28

Total: 40

y = 3x^{2} - x - 6

Solution:

Concept:

For a quadratic

y = ax^{2} + bx + c

with

a > 0

, the minimum occurs at the vertex

x = \frac{-b}{2a}

Explanation:

Given

y = 3x^{2} - x - 6

, we identify

a = 3

b = -1

, and

c = -6

Since

a = 3 > 0

, the parabola opens upward and has a minimum value.

The

x

-coordinate of the vertex is:

x = \frac{-b}{2a} = \frac{-(-1)}{2(3)} = \frac{1}{6}.

Substitute

x = \frac{1}{6}

into the equation:

y = 3\left(\frac{1}{6}\right)^{2} - \frac{1}{6} - 6.

y = 3\left(\frac{1}{36}\right) - \frac{1}{6} - 6 = \frac{1}{12} - \frac{2}{12} - 6.

y = -\frac{1}{12} - 6 = -6\frac{1}{12}.

Answer:

Minimum value is

-6\frac{1}{12}

, which is option B.

Go to Question:

Prev Question

Next Question