Question

The value of a in y = ax² +bx+c and the vertex of the parabola are given. How many x-intercepts does the parabola have? Explain how you arrived at this number.a = -3; vertex at (6,0)The parabola has x-intercept(s), because the parabola opensand the vertex isthe x-axis.

Answer 1

The sign of a indicates if the parabola opends up or down, if it is positive then it opens up, if it is negative then it opens down. In this case it is negative the it opens down.

Now, the vertex of the parabola is in the point (6,0) which means that it lies above the x-axis and since the parabola opens down it will necesarily have to x-intercepts.

Therefore:

The parabola has 2 x-intercepts, because the parabola opens downward and the vertex is above the x-axis