Y=X^2 -4x -32. Use this function and determine whether the parabola opens up or down; explain your conclusion.
Thank you.
When the leading coefficient is positive, a parabola opens up.
Leading coefficient is the coefficient of the term with the highest degree.
To determine whether the parabola opens up or down, we can look at the coefficient of the term involving the squared variable, which in this case is x^2.
The given function is y = x^2 - 4x - 32. The coefficient of x^2 is positive (1), which means the parabola opens upward.
When the coefficient of x^2 is positive, the parabola opens upward, and when it is negative, the parabola opens downward.
Therefore, the conclusion is that the parabola described by the given function opens upward.
To determine whether the parabola represented by the equation y = x^2 - 4x - 32 opens up or down, we can look at the coefficient of the x^2 term.
In the given equation, the coefficient of x^2 term is 1. Since this coefficient is positive, the parabola opens upwards.
The general form of a quadratic equation is y = ax^2 + bx + c, where "a" represents the coefficient of the x^2 term. If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards.
In this case, since the coefficient of the x^2 term is positive (1), the parabola opens upwards.