Question

Determine the direction in which the graph of the following parabola opens: f(x) = 5x² - 2x - 8?

1) Opens upwards
2) Opens downwards
3) Opens to the left
4) Opens to the right

Answer 1

The graph of the parabola f(x) = 5x² - 2x - 8 opens upwards because the coefficient of the x² term, which is 5, is positive.

The correct option is 1)

Step-by-step explanation:

To determine the direction in which the graph of the parabola opens, we need to look at the coefficient of the x2 term in the quadratic equation f(x) = 5x2 - 2x - 8.

Here, the coefficient is 5, which is a positive number. In the standard form of a quadratic equation, ax2 + bx + c, if a is positive, the parabola opens upwards, and if a is negative, it opens downwards.

Since the coefficient a in our equation is positive, the graph of the parabola opens upwards. Therefore, the correct answer is 1) Opens upwards.